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

Oct 22, 2015

$- \log \left(5 x\right) = - 3$ if and only of

$\log \left(5 x\right) = 3$

And that is true if and only if $5 x = {b}^{3}$ 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

$5 x = {10}^{3} = 1000$, so $x = \frac{1000}{5} = 200$

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

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