Solve the logarithmic equation ln(y)-2xln(x)=-8

 Exercise

$ln\left(y\right)-2xln\left(x\right)=-8$

 

We need to isolate the dependent variable $y$, we can do that by simultaneously subtracting $-2x\ln\left(x\right)$ from both sides of the equation

$\ln\left(y\right)=-8+2x\ln\left(x\right)$

 

Using the power rule of logarithms: $n\log_b(a)=\log_b(a^n)$, where $n$ equals $2$

$\ln\left(y\right)=-8+x\ln\left(x^{2}\right)$

 

Take the variable outside of the logarithm

$e^{\ln\left(y\right)}=e^{\left(-8+x\ln\left(x^{2}\right)\right)}$

 

Simplifying the logarithm

$y=e^{\left(-8+x\ln\left(x^{2}\right)\right)}$

$y=e^{\left(-8+x\ln\left(x^{2}\right)\right)}$

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