How to solve if I have ln on both sides of equation?
By Sarah Rodriguez •
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 $y$?
$\endgroup$ 62 Answers
$\begingroup$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!!!
$\endgroup$ 1 $\begingroup$$$\ln a = \ln b\\ e^{\ln a} = e^{\ln b}\\ a = b$$
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