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QUESTION

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

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