Question

How do you solve `5^-x = 250`?

Answer 1

`x=-log_5(250)`

Explanation:

Since the logarithm is the inverse function of the exponential (i.e., `log_a(a^x)=x`, you can use `log_5` to isolate the `x`:

`5^{-x}=250 \implies log_5(5^{-x})=log_5(250)`,

but `log_5(5^{-x})=-x`.

So, the equation becomes `-x=log_5(250)`, which we easily solve for `x` changing the sign.