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lg^2(100x)+lg^2(10x)=14lg(x)+15 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   2             2                       
log (100*x) + log (10*x) = 14*log(x) + 15
log⁡(10x)2+log⁡(100x)2=14log⁡(x)+15\log{\left(10 x \right)}^{2} + \log{\left(100 x \right)}^{2} = 14 \log{\left(x \right)} + 15
Simplificar
Gráfica
0.01.02.03.04.05.06.07.08.09.010.0-250250
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
          /   _____________________________\                         /   _____________________________\             /   _____________________________\                         /   _____________________________\
          |  /          2                  |                         |  /          2                  |             |  /          2                  |                         |  /          2                  |
  ____    |\/  -79 + log (10) + 42*log(10) |  7/2       ____  7/2    |\/  -79 + log (10) + 42*log(10) |     ____    |\/  -79 + log (10) + 42*log(10) |  7/2       ____  7/2    |\/  -79 + log (10) + 42*log(10) |
\/ 10 *cos|--------------------------------|*e      I*\/ 10 *e   *sin|--------------------------------|   \/ 10 *cos|--------------------------------|*e      I*\/ 10 *e   *sin|--------------------------------|
          \               2                /                         \               2                /             \               2                /                         \               2                /
------------------------------------------------- - --------------------------------------------------- + ------------------------------------------------- + ---------------------------------------------------
                       100                                                  100                                                  100                                                  100
(10e72cos⁡(−79+log⁡(10)2+42log⁡(10)2)100−10ie72sin⁡(−79+log⁡(10)2+42log⁡(10)2)100)+(10e72cos⁡(−79+log⁡(10)2+42log⁡(10)2)100+10ie72sin⁡(−79+log⁡(10)2+42log⁡(10)2)100)\left(\frac{\sqrt{10} e^{\frac{7}{2}} \cos{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100} - \frac{\sqrt{10} i e^{\frac{7}{2}} \sin{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100}\right) + \left(\frac{\sqrt{10} e^{\frac{7}{2}} \cos{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100} + \frac{\sqrt{10} i e^{\frac{7}{2}} \sin{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100}\right) 
=
          /   _____________________________\     
          |  /          2                  |     
  ____    |\/  -79 + log (10) + 42*log(10) |  7/2
\/ 10 *cos|--------------------------------|*e   
          \               2                /     
-------------------------------------------------
                        50
10e72cos⁡(−79+log⁡(10)2+42log⁡(10)2)50\frac{\sqrt{10} e^{\frac{7}{2}} \cos{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{50} 
producto
/          /   _____________________________\                         /   _____________________________\\ /          /   _____________________________\                         /   _____________________________\\
|          |  /          2                  |                         |  /          2                  || |          |  /          2                  |                         |  /          2                  ||
|  ____    |\/  -79 + log (10) + 42*log(10) |  7/2       ____  7/2    |\/  -79 + log (10) + 42*log(10) || |  ____    |\/  -79 + log (10) + 42*log(10) |  7/2       ____  7/2    |\/  -79 + log (10) + 42*log(10) ||
|\/ 10 *cos|--------------------------------|*e      I*\/ 10 *e   *sin|--------------------------------|| |\/ 10 *cos|--------------------------------|*e      I*\/ 10 *e   *sin|--------------------------------||
|          \               2                /                         \               2                /| |          \               2                /                         \               2                /|
|------------------------------------------------- - ---------------------------------------------------|*|------------------------------------------------- + ---------------------------------------------------|
\                       100                                                  100                        / \                       100                                                  100                        /
(10e72cos⁡(−79+log⁡(10)2+42log⁡(10)2)100−10ie72sin⁡(−79+log⁡(10)2+42log⁡(10)2)100)(10e72cos⁡(−79+log⁡(10)2+42log⁡(10)2)100+10ie72sin⁡(−79+log⁡(10)2+42log⁡(10)2)100)\left(\frac{\sqrt{10} e^{\frac{7}{2}} \cos{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100} - \frac{\sqrt{10} i e^{\frac{7}{2}} \sin{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100}\right) \left(\frac{\sqrt{10} e^{\frac{7}{2}} \cos{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100} + \frac{\sqrt{10} i e^{\frac{7}{2}} \sin{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100}\right) 
=
  7 
 e  
----
1000
e71000\frac{e^{7}}{1000} 
exp(7)/1000
Respuesta rápida [src] 
               /   _____________________________\                         /   _____________________________\
               |  /          2                  |                         |  /          2                  |
       ____    |\/  -79 + log (10) + 42*log(10) |  7/2       ____  7/2    |\/  -79 + log (10) + 42*log(10) |
     \/ 10 *cos|--------------------------------|*e      I*\/ 10 *e   *sin|--------------------------------|
               \               2                /                         \               2                /
x1 = ------------------------------------------------- - ---------------------------------------------------
                            100                                                  100
x1=10e72cos⁡(−79+log⁡(10)2+42log⁡(10)2)100−10ie72sin⁡(−79+log⁡(10)2+42log⁡(10)2)100x_{1} = \frac{\sqrt{10} e^{\frac{7}{2}} \cos{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100} - \frac{\sqrt{10} i e^{\frac{7}{2}} \sin{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100} 
               /   _____________________________\                         /   _____________________________\
               |  /          2                  |                         |  /          2                  |
       ____    |\/  -79 + log (10) + 42*log(10) |  7/2       ____  7/2    |\/  -79 + log (10) + 42*log(10) |
     \/ 10 *cos|--------------------------------|*e      I*\/ 10 *e   *sin|--------------------------------|
               \               2                /                         \               2                /
x2 = ------------------------------------------------- + ---------------------------------------------------
                            100                                                  100
x2=10e72cos⁡(−79+log⁡(10)2+42log⁡(10)2)100+10ie72sin⁡(−79+log⁡(10)2+42log⁡(10)2)100x_{2} = \frac{\sqrt{10} e^{\frac{7}{2}} \cos{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100} + \frac{\sqrt{10} i e^{\frac{7}{2}} \sin{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100} 
x2 = sqrt(10)*exp(7/2)*cos(sqrt(-79 + log(10)^2 + 42*log(10))/2)/100 + sqrt(10)*i*exp(7/2)*sin(sqrt(-79 + log(10)^2 + 42*log(10))/2)/100
Respuesta numérica [src] 
x1 = -0.771111469526577 + 0.708533880624647*i
x2 = -0.771111469526577 - 0.708533880624647*i
x2 = -0.771111469526577 - 0.708533880624647*i
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