# What is x if lnx + ln5x^2 = 10?

Nov 10, 2015

First, you should use the logarithm rule
${\log}_{a} \left(x\right) + {\log}_{a} \left(y\right) = {\log}_{a} \left(x \cdot y\right)$

Here, it gives you:
" ln x + ln 5 x^2 = 10
<=> " ln( x * 5 x^2) = 10
<=> " ln(5 x^3) = 10

Now, you can exponentiate both sides to get rid of the $\ln$:

<=> " e^(ln(5x^3)) = e^10

... remember that $e$ and $\ln$ are inverse functions...

<=> " 5x^3 = e^10
<=> " x^3 = (e^10) / 5
<=> " x = root(3)((e^10) / 5)