How do you solve $ln (\frac{1}{e^{5}}) = x$ $ln (1/e^5)=x$ ?

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Answer 1 · 2016-07-22T09:22:01

The soln. is # : x=-5

$ln (\frac{1}{e^{5}}) = x$ $ln(1/e^5)=x$

We know that, $\frac{1}{e^{a}} = e^{- a}, and, {ln e}^{b} = b$ $1/e^a=e^(-a), and, lne^b=b$

$:. ln(e^(-5))=ln (e^x))............(1)$

Now, $ln$ fun. is $1-1$ . Hence, $(1) rArre^(-5)=e^x$ .

Again, fun. $e^x$ is $1-1$ , so, $x=-5$ is the soln.

How do you solve ln (1/e^5)=xln(1e5)=xln (1/e^5)=x?