# How do you evaluate log_[16]1 ?

Mar 22, 2016

${\log}_{16} 1 = 0$

#### Explanation:

${\log}_{16} 1$
$= \log \frac{1}{\log} 16$-> use change of base property ${\log}_{b} x = \log \frac{x}{\log} b$
$= \frac{0}{\log} 16$->$\log 1 = 0$
$= 0$

Mar 22, 2016

0

#### Explanation:

By definition $\log 1$ to any base is equal to $0$.

Proof:
Let ${\log}_{16} 1 = n$
By definition of logarithmic function

${16}^{n} = 1$, This is true only if $n = 0$