# How do you evaluate log 1?

Jun 11, 2015

$\log 1 = 0$

#### Explanation:

You. basically. want to find the number $a$ that used as exponent of the base $b$ of your log gives $1$:
${\log}_{b} 1 = a$
i.e.:
${b}^{a} = 1$
${b}^{0} = 1$

$a = 0$
because a number to the power zero gives you $1$.

Jun 11, 2015

${\log}_{10} 1$ can be evaluated like so:

$\log 1 = x$

${10}^{{\log}_{10} 1} = {10}^{x}$

10 raised to a log base 10 of something is that something.

$1 = {10}^{x}$

Anything raised to the 0 is 1.

$x = 0$

Thus, $\log 1 = 0$.