# How do you evaluate log_15 1?

Aug 31, 2016

Zero

#### Explanation:

${2}^{3} = 8$ which can also be written as ${\log}_{2} \left(8\right) = 3$

This is I think quite easy to remember

So given ${\log}_{15} \left(1\right) = x$ where you want to find X
Rewrite as ${15}^{x} = 1$

Any number to the power of zero =1

So X=1

Aug 31, 2016

${\log}_{15} 1 = 0$

#### Explanation:

The question we need to ask with log format is..

"What index/power of 15 will give 1?"

Any base raised to the power of 0 will give 1.

${15}^{0} = 1$

Log form and index form are interchangeable.

${\log}_{15} 1 = 0 \Leftrightarrow {15}^{0} = 1$

Remember that ${0}^{0}$ is undefined., so $\log 0$ is undefined.