Question

What is x if `-log(5x) = -3`?

Answer 1

`-log(5x) = -3` if and only of

`log(5x) = 3`

And that is true if and only if `5x = b^3` for whatever base you intend by `log`.

Traditionally `log` without a subscript meant the Common Logarithm which is the base 10 log, so we would have

`5x=10^3 = 1000`, so `x=1000/5 = 200`

Many people now use `log` to mean the Natural Log (log base `e`)

In that case we get `5x=e^3` so `x = e^3/5`
(Which can be found without a table or a calculator, but it's a bit tedious.)