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La ecuación:
Ecuación 2x=1
Ecuación 3^x=6
Ecuación x:(-6)=55
Ecuación 3+11y=203+y
Expresar {x} en función de y en la ecuación:
-17*x+6*y=14
20*x-8*y=13
4*x-1*y=12
-1*x+14*y=1
Expresiones idénticas
(sesenta y cuatro)^(dos -x)=(treinta y dos)^(x+ tres)
(64) en el grado (2 menos x) es igual a (32) en el grado (x más 3)
(sesenta y cuatro) en el grado (dos menos x) es igual a (treinta y dos) en el grado (x más tres)
(64)(2-x)=(32)(x+3)
642-x=32x+3
64^2-x=32^x+3
Expresiones semejantes
(64)^(2-x)=(32)^(x-3)
(64)^(2+x)=(32)^(x+3)

(64)^(2-x)=(32)^(x+3) la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

  2 - x     x + 3
64      = 32

64^{2 - x} = 32^{x + 3}

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

                                                                                                                              /         /   /3*pi\\\            /          /   /pi\\\                                             /          /   /pi\\\                                             /         /   /pi\\\                                                 /          /   /5*pi\\\                   
                                                                                                                              |         |sin|----|||            |          |sin|--|||                                             |          |cos|--|||                                             |         |cos|--|||                                                 |          |cos|----|||                   
                                                                                                                              |         |   \ 11 /||            |          |   \11/||                                             |          |   \22/||                                             |         |   \22/||                                                 |          |   \ 22 /||                   
                                                                                                                  / 8/11\   I*|pi - atan|---------||          I*|-pi + atan|-------||             /    _____________________\   I*|-pi + atan|-------||             /    _____________________\   I*|pi - atan|-------||             /    _________________________\   I*|-pi + atan|---------||                   
                                                                                                                  |2    |     |         |   /3*pi\||            |          |   /pi\||             |   /    2/pi\      2/pi\ |     |          |   /pi\||             |   /    2/pi\      2/pi\ |     |         |   /pi\||             |   /    2/5*pi\      2/5*pi\ |     |          |   /5*pi\||                   
                                                                                                               log|-----|     |         |cos|----|||            |          |cos|--|||          log|  /  cos |--| + sin |--| |     |          |sin|--|||          log|  /  cos |--| + sin |--| |     |         |sin|--|||          log|  /  cos |----| + sin |----| |     |          |sin|----|||                   
  3        log(8)      2*pi*I        log(8)      4*pi*I        log(8)      2*pi*I        log(8)      4*pi*I       \  2  /     \         \   \ 11 ///     3      \          \   \11///     3       \\/       \22/       \22/ /     \          \   \22///     3       \\/       \22/       \22/ /     \         \   \22///     3       \\/       \ 22 /       \ 22 / /     \          \   \ 22 ///     3     10*pi*I 
- -- + - --------- + --------- + - --------- + --------- + - --------- - --------- + - --------- - --------- + ---------- + ------------------------ + - -- + ----------------------- + - -- + ------------------------------ + ----------------------- + - -- + ------------------------------ + ---------------------- + - -- + ---------------------------------- + ------------------------- + - -- + ---------
  11     11*log(2)   11*log(2)     11*log(2)   11*log(2)     11*log(2)   11*log(2)     11*log(2)   11*log(2)     log(2)              log(2)              11            log(2)             11               log(2)                        log(2)             11               log(2)                       log(2)             11                 log(2)                           log(2)              11   11*log(2)

\left(\left(- \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{5 \pi}{22} \right)} + \cos^{2}{\left(\frac{5 \pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{5 \pi}{22} \right)}}{\sin{\left(\frac{5 \pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) + \left(\left(\left(- \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{22} \right)} + \cos^{2}{\left(\frac{\pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{22} \right)}}{\sin{\left(\frac{\pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) + \left(\left(- \frac{3}{11} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{11} \right)}}{\cos{\left(\frac{\pi}{11} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) + \left(\left(\left(- \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} - \frac{4 i \pi}{11 \log{\left(2 \right)}}\right) + \left(\left(- \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} - \frac{2 i \pi}{11 \log{\left(2 \right)}}\right) + \left(\left(- \frac{3}{11} + \left(- \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} + \frac{2 i \pi}{11 \log{\left(2 \right)}}\right)\right) + \left(- \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} + \frac{4 i \pi}{11 \log{\left(2 \right)}}\right)\right)\right)\right) + \left(\frac{\log{\left(\frac{2^{\frac{8}{11}}}{2} \right)}}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{11} \right)}}{\cos{\left(\frac{3 \pi}{11} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right)\right)\right)\right) + \left(- \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{22} \right)} + \cos^{2}{\left(\frac{\pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{22} \right)}}{\sin{\left(\frac{\pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right)\right)\right) + \left(- \frac{3}{11} + \frac{10 i \pi}{11 \log{\left(2 \right)}}\right)

                                                                                                          /         /   /3*pi\\\     /         /   /pi\\\     /          /   /pi\\\     /          /   /pi\\\     /          /   /5*pi\\\            
                                                                                                          |         |sin|----|||     |         |cos|--|||     |          |sin|--|||     |          |cos|--|||     |          |cos|----|||            
                                                                                                          |         |   \ 11 /||     |         |   \22/||     |          |   \11/||     |          |   \22/||     |          |   \ 22 /||            
          /    _________________________\      / 8/11\        /    _____________________\               I*|pi - atan|---------||   I*|pi - atan|-------||   I*|-pi + atan|-------||   I*|-pi + atan|-------||   I*|-pi + atan|---------||            
          |   /    2/5*pi\      2/5*pi\ |      |2    |        |   /    2/pi\      2/pi\ |                 |         |   /3*pi\||     |         |   /pi\||     |          |   /pi\||     |          |   /pi\||     |          |   /5*pi\||            
       log|  /  cos |----| + sin |----| |   log|-----|   2*log|  /  cos |--| + sin |--| |                 |         |cos|----|||     |         |sin|--|||     |          |cos|--|||     |          |sin|--|||     |          |sin|----|||            
  18      \\/       \ 22 /       \ 22 / /      \  2  /        \\/       \22/       \22/ /    4*log(8)     \         \   \ 11 ///     \         \   \22///     \          \   \11///     \          \   \22///     \          \   \ 22 ///    10*pi*I 
- -- + ---------------------------------- + ---------- + -------------------------------- - --------- + ------------------------ + ---------------------- + ----------------------- + ----------------------- + ------------------------- + ---------
  11                 log(2)                   log(2)                  log(2)                11*log(2)            log(2)                    log(2)                    log(2)                    log(2)                     log(2)            11*log(2)

- \frac{18}{11} - \frac{4 \log{\left(8 \right)}}{11 \log{\left(2 \right)}} + \frac{\log{\left(\frac{2^{\frac{8}{11}}}{2} \right)}}{\log{\left(2 \right)}} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{5 \pi}{22} \right)} + \cos^{2}{\left(\frac{5 \pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{2 \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{22} \right)} + \cos^{2}{\left(\frac{\pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{11} \right)}}{\cos{\left(\frac{\pi}{11} \right)}} \right)}\right)}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{5 \pi}{22} \right)}}{\sin{\left(\frac{5 \pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{22} \right)}}{\sin{\left(\frac{\pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{22} \right)}}{\sin{\left(\frac{\pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{11} \right)}}{\cos{\left(\frac{3 \pi}{11} \right)}} \right)}\right)}{\log{\left(2 \right)}} + \frac{10 i \pi}{11 \log{\left(2 \right)}}

producto

                                                                                                           /               /         /   /3*pi\\\\ /         /          /   /pi\\\\ /                                          /          /   /pi\\\\ /                                          /         /   /pi\\\\ /                                              /          /   /5*pi\\\\                   
                                                                                                           |               |         |sin|----|||| |         |          |sin|--|||| |                                          |          |cos|--|||| |                                          |         |cos|--|||| |                                              |          |cos|----||||                   
                                                                                                           |               |         |   \ 11 /||| |         |          |   \11/||| |                                          |          |   \22/||| |                                          |         |   \22/||| |                                              |          |   \ 22 /|||                   
                                                                                                           |   / 8/11\   I*|pi - atan|---------||| |       I*|-pi + atan|-------||| |          /    _____________________\   I*|-pi + atan|-------||| |          /    _____________________\   I*|pi - atan|-------||| |          /    _________________________\   I*|-pi + atan|---------|||                   
   /    log(8)      2*pi*I \                                                                               |   |2    |     |         |   /3*pi\||| |         |          |   /pi\||| |          |   /    2/pi\      2/pi\ |     |          |   /pi\||| |          |   /    2/pi\      2/pi\ |     |         |   /pi\||| |          |   /    2/5*pi\      2/5*pi\ |     |          |   /5*pi\|||                   
-3*|- --------- + ---------|                                                                               |log|-----|     |         |cos|----|||| |         |          |cos|--|||| |       log|  /  cos |--| + sin |--| |     |          |sin|--|||| |       log|  /  cos |--| + sin |--| |     |         |sin|--|||| |       log|  /  cos |----| + sin |----| |     |          |sin|----||||                   
   \  11*log(2)   11*log(2)/ /    log(8)      4*pi*I \ /    log(8)      2*pi*I \ /    log(8)      4*pi*I \ |   \  2  /     \         \   \ 11 ///| |  3      \          \   \11///| |  3       \\/       \22/       \22/ /     \          \   \22///| |  3       \\/       \22/       \22/ /     \         \   \22///| |  3       \\/       \ 22 /       \ 22 / /     \          \   \ 22 ///| /  3     10*pi*I \
----------------------------*|- --------- + ---------|*|- --------- - ---------|*|- --------- - ---------|*|---------- + ------------------------|*|- -- + -----------------------|*|- -- + ------------------------------ + -----------------------|*|- -- + ------------------------------ + ----------------------|*|- -- + ---------------------------------- + -------------------------|*|- -- + ---------|
             11              \  11*log(2)   11*log(2)/ \  11*log(2)   11*log(2)/ \  11*log(2)   11*log(2)/ \  log(2)              log(2)         / \  11            log(2)        / \  11               log(2)                        log(2)        / \  11               log(2)                       log(2)        / \  11                 log(2)                           log(2)         / \  11   11*log(2)/

- \frac{3 \left(- \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} + \frac{2 i \pi}{11 \log{\left(2 \right)}}\right)}{11} \left(- \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} + \frac{4 i \pi}{11 \log{\left(2 \right)}}\right) \left(- \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} - \frac{2 i \pi}{11 \log{\left(2 \right)}}\right) \left(- \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} - \frac{4 i \pi}{11 \log{\left(2 \right)}}\right) \left(\frac{\log{\left(\frac{2^{\frac{8}{11}}}{2} \right)}}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{11} \right)}}{\cos{\left(\frac{3 \pi}{11} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) \left(- \frac{3}{11} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{11} \right)}}{\cos{\left(\frac{\pi}{11} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) \left(- \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{22} \right)} + \cos^{2}{\left(\frac{\pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{22} \right)}}{\sin{\left(\frac{\pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) \left(- \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{22} \right)} + \cos^{2}{\left(\frac{\pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{22} \right)}}{\sin{\left(\frac{\pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) \left(- \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{5 \pi}{22} \right)} + \cos^{2}{\left(\frac{5 \pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{5 \pi}{22} \right)}}{\sin{\left(\frac{5 \pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}\right) \left(- \frac{3}{11} + \frac{10 i \pi}{11 \log{\left(2 \right)}}\right)

 /          10                 10             2    8                 4    6                  6    4                  8    2   \ 
-\177147*log  (2) + 44236800*pi   + 4330260*pi *log (2) + 35796816*pi *log (2) + 118895040*pi *log (2) + 145677312*pi *log (2)/ 
--------------------------------------------------------------------------------------------------------------------------------
                                                                     10                                                         
                                                     285311670611*log  (2)

- \frac{177147 \log{\left(2 \right)}^{10} + 4330260 \pi^{2} \log{\left(2 \right)}^{8} + 35796816 \pi^{4} \log{\left(2 \right)}^{6} + 118895040 \pi^{6} \log{\left(2 \right)}^{4} + 145677312 \pi^{8} \log{\left(2 \right)}^{2} + 44236800 \pi^{10}}{285311670611 \log{\left(2 \right)}^{10}}

-(177147*log(2)^10 + 44236800*pi^10 + 4330260*pi^2*log(2)^8 + 35796816*pi^4*log(2)^6 + 118895040*pi^6*log(2)^4 + 145677312*pi^8*log(2)^2)/(285311670611*log(2)^10)

Respuesta rápida [src]

x1 = -3/11

x_{1} = - \frac{3}{11}

         log(8)      2*pi*I 
x2 = - --------- + ---------
       11*log(2)   11*log(2)

x_{2} = - \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} + \frac{2 i \pi}{11 \log{\left(2 \right)}}

         log(8)      4*pi*I 
x3 = - --------- + ---------
       11*log(2)   11*log(2)

x_{3} = - \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} + \frac{4 i \pi}{11 \log{\left(2 \right)}}

         log(8)      2*pi*I 
x4 = - --------- - ---------
       11*log(2)   11*log(2)

x_{4} = - \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} - \frac{2 i \pi}{11 \log{\left(2 \right)}}

         log(8)      4*pi*I 
x5 = - --------- - ---------
       11*log(2)   11*log(2)

x_{5} = - \frac{\log{\left(8 \right)}}{11 \log{\left(2 \right)}} - \frac{4 i \pi}{11 \log{\left(2 \right)}}

                    /         /   /3*pi\\\
                    |         |sin|----|||
                    |         |   \ 11 /||
        / 8/11\   I*|pi - atan|---------||
        |2    |     |         |   /3*pi\||
     log|-----|     |         |cos|----|||
        \  2  /     \         \   \ 11 ///
x6 = ---------- + ------------------------
       log(2)              log(2)

x_{6} = \frac{\log{\left(\frac{2^{\frac{8}{11}}}{2} \right)}}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{11} \right)}}{\cos{\left(\frac{3 \pi}{11} \right)}} \right)}\right)}{\log{\left(2 \right)}}

              /          /   /pi\\\
              |          |sin|--|||
              |          |   \11/||
            I*|-pi + atan|-------||
              |          |   /pi\||
              |          |cos|--|||
       3      \          \   \11///
x7 = - -- + -----------------------
       11            log(2)

x_{7} = - \frac{3}{11} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{11} \right)}}{\cos{\left(\frac{\pi}{11} \right)}} \right)}\right)}{\log{\left(2 \right)}}

                                               /          /   /pi\\\
                                               |          |cos|--|||
                                               |          |   \22/||
               /    _____________________\   I*|-pi + atan|-------||
               |   /    2/pi\      2/pi\ |     |          |   /pi\||
            log|  /  cos |--| + sin |--| |     |          |sin|--|||
       3       \\/       \22/       \22/ /     \          \   \22///
x8 = - -- + ------------------------------ + -----------------------
       11               log(2)                        log(2)

x_{8} = - \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{22} \right)} + \cos^{2}{\left(\frac{\pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{22} \right)}}{\sin{\left(\frac{\pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}

                                               /         /   /pi\\\
                                               |         |cos|--|||
                                               |         |   \22/||
               /    _____________________\   I*|pi - atan|-------||
               |   /    2/pi\      2/pi\ |     |         |   /pi\||
            log|  /  cos |--| + sin |--| |     |         |sin|--|||
       3       \\/       \22/       \22/ /     \         \   \22///
x9 = - -- + ------------------------------ + ----------------------
       11               log(2)                       log(2)

x_{9} = - \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{22} \right)} + \cos^{2}{\left(\frac{\pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{22} \right)}}{\sin{\left(\frac{\pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}

                                                    /          /   /5*pi\\\
                                                    |          |cos|----|||
                                                    |          |   \ 22 /||
                /    _________________________\   I*|-pi + atan|---------||
                |   /    2/5*pi\      2/5*pi\ |     |          |   /5*pi\||
             log|  /  cos |----| + sin |----| |     |          |sin|----|||
        3       \\/       \ 22 /       \ 22 / /     \          \   \ 22 ///
x10 = - -- + ---------------------------------- + -------------------------
        11                 log(2)                           log(2)

x_{10} = - \frac{3}{11} + \frac{\log{\left(\sqrt{\sin^{2}{\left(\frac{5 \pi}{22} \right)} + \cos^{2}{\left(\frac{5 \pi}{22} \right)}} \right)}}{\log{\left(2 \right)}} + \frac{i \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{5 \pi}{22} \right)}}{\sin{\left(\frac{5 \pi}{22} \right)}} \right)}\right)}{\log{\left(2 \right)}}

        3     10*pi*I 
x11 = - -- + ---------
        11   11*log(2)

x_{11} = - \frac{3}{11} + \frac{10 i \pi}{11 \log{\left(2 \right)}}

x11 = -3/11 + 10*i*pi/(11*log(2))

Respuesta numérica [src]

x1 = -0.272727272727273

x2 = -0.272727272727273 + 0.824065480332217*i

x3 = -0.272727272727273 + 1.64813096066443*i

x4 = -0.272727272727273 - 0.824065480332217*i

x5 = -0.272727272727273 - 1.64813096066443*i

x6 = -0.272727272727273 + 3.29626192132887*i

x7 = -0.272727272727273 - 4.12032740166109*i

x8 = -0.272727272727273 - 2.47219644099665*i

x9 = -0.272727272727273 + 2.47219644099665*i

x10 = -0.272727272727273 - 3.29626192132887*i

x11 = -0.272727272727273 + 4.12032740166109*i

x11 = -0.272727272727273 + 4.12032740166109*i

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(64)^(2-x)=(32)^(x+3) la ecuación

Solución numérica:

Solución