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ln(x)*10^6=(ln(n))^y la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                    y   
log(x)*1000000 = log (n)
1000000log⁡(x)=log⁡(n)y1000000 \log{\left(x \right)} = \log{\left(n \right)}^{y}
Simplificar
Solución detallada
Tenemos la ecuación:
1000000log⁡(x)=log⁡(n)y1000000 \log{\left(x \right)} = \log{\left(n \right)}^{y}
o
−log⁡(n)y+1000000log⁡(x)=0- \log{\left(n \right)}^{y} + 1000000 \log{\left(x \right)} = 0
o
−log⁡(n)y=−1000000log⁡(x)- \log{\left(n \right)}^{y} = - 1000000 \log{\left(x \right)}
o
log⁡(n)y=1000000log⁡(x)\log{\left(n \right)}^{y} = 1000000 \log{\left(x \right)}
- es la ecuación exponencial más simple
Sustituimos
v=log⁡(n)yv = \log{\left(n \right)}^{y}
obtendremos
v−1000000log⁡(x)=0v - 1000000 \log{\left(x \right)} = 0
o
v−1000000log⁡(x)=0v - 1000000 \log{\left(x \right)} = 0
hacemos cambio inverso
log⁡(n)y=v\log{\left(n \right)}^{y} = v
o
y=log⁡(v)log⁡(log⁡(n))y = \frac{\log{\left(v \right)}}{\log{\left(\log{\left(n \right)} \right)}}
Entonces la respuesta definitiva es
y1=log⁡(1000000log⁡(x))log⁡(log⁡(n))=log⁡(1000000log⁡(x))log⁡(log⁡(n))y_{1} = \frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}} = \frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}
Gráfica
Suma y producto de raíces [src] 
suma
    /log(1000000*log(x))\     /log(1000000*log(x))\
I*im|-------------------| + re|-------------------|
    \    log(log(n))    /     \    log(log(n))    /
re⁡(log⁡(1000000log⁡(x))log⁡(log⁡(n)))+iim⁡(log⁡(1000000log⁡(x))log⁡(log⁡(n)))\operatorname{re}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)} + i \operatorname{im}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)} 
=
    /log(1000000*log(x))\     /log(1000000*log(x))\
I*im|-------------------| + re|-------------------|
    \    log(log(n))    /     \    log(log(n))    /
re⁡(log⁡(1000000log⁡(x))log⁡(log⁡(n)))+iim⁡(log⁡(1000000log⁡(x))log⁡(log⁡(n)))\operatorname{re}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)} + i \operatorname{im}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)} 
producto
    /log(1000000*log(x))\     /log(1000000*log(x))\
I*im|-------------------| + re|-------------------|
    \    log(log(n))    /     \    log(log(n))    /
re⁡(log⁡(1000000log⁡(x))log⁡(log⁡(n)))+iim⁡(log⁡(1000000log⁡(x))log⁡(log⁡(n)))\operatorname{re}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)} + i \operatorname{im}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)} 
=
    /log(1000000*log(x))\     /log(1000000*log(x))\
I*im|-------------------| + re|-------------------|
    \    log(log(n))    /     \    log(log(n))    /
re⁡(log⁡(1000000log⁡(x))log⁡(log⁡(n)))+iim⁡(log⁡(1000000log⁡(x))log⁡(log⁡(n)))\operatorname{re}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)} + i \operatorname{im}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)} 
i*im(log(1000000*log(x))/log(log(n))) + re(log(1000000*log(x))/log(log(n)))
Respuesta rápida [src] 
         /log(1000000*log(x))\     /log(1000000*log(x))\
y1 = I*im|-------------------| + re|-------------------|
         \    log(log(n))    /     \    log(log(n))    /
y1=re⁡(log⁡(1000000log⁡(x))log⁡(log⁡(n)))+iim⁡(log⁡(1000000log⁡(x))log⁡(log⁡(n)))y_{1} = \operatorname{re}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)} + i \operatorname{im}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)} 
y1 = re(log(1000000*log(x))/log(log(n))) + i*im(log(1000000*log(x))/log(log(n)))
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