Question

How do you solve `5^-x = 3`?

Answer 1

Using the log.

Explanation:

To solve the equations where the `x` is in the exponent, the trick is to do the logarithms.

`5^(-x)=3`

`log(5^(-x))=log(3)`

we then apply the property of the logarithm where the exponent in the log goes in front multiplying.

`-xlog(5)=log(3)`

`x=-log(3)/log(5)\approx-0.68`.