Question

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

Answer 1

Take the natural log of both sides and solve.

Explanation:

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