Sr Examen

Otras calculadoras

25^(x-1)+sqrt(1/(25^(-2*x)))=475+(1/5)^(1-2*x) la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
               ________                  
  x - 1       /   1              -1 + 2*x
25      +    /  ------  = 475 + 5        
            /     -2*x                   
          \/    25
25x−1+125−2x=(15)1−2x+47525^{x - 1} + \sqrt{\frac{1}{25^{- 2 x}}} = \left(\frac{1}{5}\right)^{1 - 2 x} + 475
Simplificar
Gráfica
02468-8-6-4-2100100000000000000000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
   /              1   \                                                                           
   |            ------|                                                      /     _____\         
   |            log(5)|      /11875\                 /11875\                 |25*\/ 399 |         
   |/     _____\      |   log|-----|              log|-----|              log|----------|         
   ||25*\/ 399 |      |      \  29 /     pi*I        \  29 /     pi*I        \    21    /    pi*I 
log||----------|      | + ---------- - -------- + ---------- + -------- + --------------- + ------
   \\    21    /      /    2*log(5)    2*log(5)    2*log(5)    2*log(5)        log(5)       log(5)
((log⁡((2539921)1log⁡(5))+(log⁡(1187529)2log⁡(5)−iπ2log⁡(5)))+(log⁡(1187529)2log⁡(5)+iπ2log⁡(5)))+(log⁡(2539921)log⁡(5)+iπlog⁡(5))\left(\left(\log{\left(\left(\frac{25 \sqrt{399}}{21}\right)^{\frac{1}{\log{\left(5 \right)}}} \right)} + \left(\frac{\log{\left(\frac{11875}{29} \right)}}{2 \log{\left(5 \right)}} - \frac{i \pi}{2 \log{\left(5 \right)}}\right)\right) + \left(\frac{\log{\left(\frac{11875}{29} \right)}}{2 \log{\left(5 \right)}} + \frac{i \pi}{2 \log{\left(5 \right)}}\right)\right) + \left(\frac{\log{\left(\frac{25 \sqrt{399}}{21} \right)}}{\log{\left(5 \right)}} + \frac{i \pi}{\log{\left(5 \right)}}\right) 
=
                                           /              1   \
                /     _____\               |            ------|
   /11875\      |25*\/ 399 |               |            log(5)|
log|-----|   log|----------|               |/     _____\      |
   \  29 /      \    21    /    pi*I       ||25*\/ 399 |      |
---------- + --------------- + ------ + log||----------|      |
  log(5)          log(5)       log(5)      \\    21    /      /
log⁡(2539921)log⁡(5)+log⁡((2539921)1log⁡(5))+log⁡(1187529)log⁡(5)+iπlog⁡(5)\frac{\log{\left(\frac{25 \sqrt{399}}{21} \right)}}{\log{\left(5 \right)}} + \log{\left(\left(\frac{25 \sqrt{399}}{21}\right)^{\frac{1}{\log{\left(5 \right)}}} \right)} + \frac{\log{\left(\frac{11875}{29} \right)}}{\log{\left(5 \right)}} + \frac{i \pi}{\log{\left(5 \right)}} 
producto
   /              1   \                                                                           
   |            ------|                                                 /   /     _____\         \
   |            log(5)| /   /11875\           \ /   /11875\           \ |   |25*\/ 399 |         |
   |/     _____\      | |log|-----|           | |log|-----|           | |log|----------|         |
   ||25*\/ 399 |      | |   \  29 /     pi*I  | |   \  29 /     pi*I  | |   \    21    /    pi*I |
log||----------|      |*|---------- - --------|*|---------- + --------|*|--------------- + ------|
   \\    21    /      / \ 2*log(5)    2*log(5)/ \ 2*log(5)    2*log(5)/ \     log(5)       log(5)/
(log⁡(1187529)2log⁡(5)−iπ2log⁡(5))log⁡((2539921)1log⁡(5))(log⁡(1187529)2log⁡(5)+iπ2log⁡(5))(log⁡(2539921)log⁡(5)+iπlog⁡(5))\left(\frac{\log{\left(\frac{11875}{29} \right)}}{2 \log{\left(5 \right)}} - \frac{i \pi}{2 \log{\left(5 \right)}}\right) \log{\left(\left(\frac{25 \sqrt{399}}{21}\right)^{\frac{1}{\log{\left(5 \right)}}} \right)} \left(\frac{\log{\left(\frac{11875}{29} \right)}}{2 \log{\left(5 \right)}} + \frac{i \pi}{2 \log{\left(5 \right)}}\right) \left(\frac{\log{\left(\frac{25 \sqrt{399}}{21} \right)}}{\log{\left(5 \right)}} + \frac{i \pi}{\log{\left(5 \right)}}\right) 
=
                                                                     /                1    \
                                                                     |            ---------|
                                                                     |                 4   |
                                                                     |            4*log (5)|
                    /          /     _____\\                         |/     _____\         |
/          /11875\\ |          |25*\/ 399 || /           /11875\\    ||25*\/ 399 |         |
|pi*I + log|-----||*|pi*I + log|----------||*|-pi*I + log|-----||*log||----------|         |
\          \  29 // \          \    21    // \           \  29 //    \\    21    /         /
(log⁡(1187529)−iπ)(log⁡(1187529)+iπ)(log⁡(2539921)+iπ)log⁡((2539921)14log⁡(5)4)\left(\log{\left(\frac{11875}{29} \right)} - i \pi\right) \left(\log{\left(\frac{11875}{29} \right)} + i \pi\right) \left(\log{\left(\frac{25 \sqrt{399}}{21} \right)} + i \pi\right) \log{\left(\left(\frac{25 \sqrt{399}}{21}\right)^{\frac{1}{4 \log{\left(5 \right)}^{4}}} \right)} 
(pi*i + log(11875/29))*(pi*i + log(25*sqrt(399)/21))*(-pi*i + log(11875/29))*log((25*sqrt(399)/21)^(1/(4*log(5)^4)))
Respuesta rápida [src] 
        /              1   \
        |            ------|
        |            log(5)|
        |/     _____\      |
        ||25*\/ 399 |      |
x1 = log||----------|      |
        \\    21    /      /
x1=log⁡((2539921)1log⁡(5))x_{1} = \log{\left(\left(\frac{25 \sqrt{399}}{21}\right)^{\frac{1}{\log{\left(5 \right)}}} \right)} 
        /11875\           
     log|-----|           
        \  29 /     pi*I  
x2 = ---------- - --------
      2*log(5)    2*log(5)
x2=log⁡(1187529)2log⁡(5)−iπ2log⁡(5)x_{2} = \frac{\log{\left(\frac{11875}{29} \right)}}{2 \log{\left(5 \right)}} - \frac{i \pi}{2 \log{\left(5 \right)}} 
        /11875\           
     log|-----|           
        \  29 /     pi*I  
x3 = ---------- + --------
      2*log(5)    2*log(5)
x3=log⁡(1187529)2log⁡(5)+iπ2log⁡(5)x_{3} = \frac{\log{\left(\frac{11875}{29} \right)}}{2 \log{\left(5 \right)}} + \frac{i \pi}{2 \log{\left(5 \right)}} 
        /     _____\         
        |25*\/ 399 |         
     log|----------|         
        \    21    /    pi*I 
x4 = --------------- + ------
          log(5)       log(5)
x4=log⁡(2539921)log⁡(5)+iπlog⁡(5)x_{4} = \frac{\log{\left(\frac{25 \sqrt{399}}{21} \right)}}{\log{\left(5 \right)}} + \frac{i \pi}{\log{\left(5 \right)}} 
x4 = log(25*sqrt(399)/21)/log(5) + i*pi/log(5)
Respuesta numérica [src] 
x1 = 1.86863213313383 - 0.975990632915586*i
x2 = 1.86863213313383 + 0.975990632915586*i
x3 = 1.9689073254135 + 1.95198126583117*i
x4 = 1.9689073254135
x4 = 1.9689073254135
    © Sr Examen – Калькулятор