How do you evaluate $log (1/100)$ ?

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Answer 1 · 2016-03-11T02:55:25

It is

$log (1/100)=log(1/10^2)=log1-log10^2=-2log10=-2$

Note that $log_10 10=1$

Answer 2 · 2016-03-11T02:58:08

$log(1/100)=-2$

First, lets assume that the base of the logarithm is $10$ , sometimes written $log_(10)$ . Next, we'll simplify by using the knowledge that

$log(x^a)=a*log(x)$

We can convert the $1/100$ in the expression to a power of $10$ :

$log(1/100)=log(100^(-1))=log((10^2)^(-1))=log(10^-2)$

Which we can rewrite as

$-2*log(10)=-2$

since $log_10(10)=1$

How do you evaluate log (1/100)log (1/100)?