How to solve if I have ln on both sides of equation?

Question

I thought this would be a common problem but googling hasn't helped.

If I have $\ln(ex)=\ln(y) $ what the next step to solve for $y$?

Answer 1

If you notice that $y = e^{\ln y}$, then you have $y = e^{\ln (ex)}$ as well; but $e^{\ln(ex)} = ex$, so $y = ex$!

And if it is $\ln y = \ln (e^x)$, you can still say $y = e^{\ln y}$ so $y = e^{\ln (e^x)} = e^x$!

Hope this helps! Cheerio,

and as always,

Fiat Lux!!!

Answer 2

$$\ln a = \ln b\\ e^{\ln a} = e^{\ln b}\\ a = b$$