# How do you evaluate log 0.5915?

Sep 2, 2015

${\log}_{10} 0.5915 = - 0.22805$

#### Explanation:

Possibly not the kind of answer you were hoping for, but the only reasonable way to do this is to use a calculator (that has a log function).

You are looking for a value, $x$ such that
$\textcolor{w h i t e}{\text{XXXX}} {10}^{x} = 0.5915$

Since ${10}^{0} = 1 \mathmr{and} {10}^{- 1} = 0.1$
and since $1 > 0.5915 > 0.1$
$\rightarrow \textcolor{w h i t e}{\text{XXXX}} 0 > x > - 1$

We could try different values between $0 \mathmr{and} - 1$ as the exponent, but without a calculator (or similar technology) such evaluations are too time consuming to be reasonable.