How do you solve $e^(-3n)=83$ ?

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Answer 1 · 2017-05-09T15:31:31

Take the natural log of both sides and solve.

Note that $ln(x)$ is the natural logarithm or $log_e(x)$ .

First, we can take the natural log of both sides to get $n$ out of the exponent:
$ln(e^(-3n))=ln(83)$

Since the $ln$ and the $e$ cancel, we get:
$-3n=ln(83)$

Dividing $-3$ from both sides, we get our value of $n$ as:
$n=-ln(83)/3~~-1.473$ rounded to three decimal places

How do you solve e^(-3n)=83e^(-3n)=83?