# How do you evaluate log100?

Aug 22, 2016

2

#### Explanation:

Using the $\textcolor{b l u e}{\text{law of logarithms}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\log}_{b} a = n \Leftrightarrow a = {b}^{n}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

When the log without any base indicated,is used, it usually assumes base 10.

$\Rightarrow {\log}_{10} 100 = n \Rightarrow 100 = {10}^{n} \Rightarrow n = 2$

Aug 22, 2016

${\log}_{10} 100 = 2$

#### Explanation:

A log expression asks a question....

If no base is shown, it is assumed to be 10

In this case ${\log}_{10} 100$ asks...

"What power of 10 is 100?"
"100 is which power of 10?"
"Which index of 10 will make 100?"

Log form and index form are interchangeable.

We know that ${10}^{2} = 100$ , so the answer is 2.

${\log}_{10} 100 = 2$

IN the same way:
${\log}_{5} 125 = 3 \text{ } {5}^{3} = 125$

${\log}_{6} 36 = 2$

${\log}_{81} 3 = \frac{1}{4} \text{ "root4(81) = 3" or } {81}^{\frac{1}{4}} = 3$