# What is the logarithm of one?

What is the logarithm of one?

log_{b}(1) = ?

The logarithmic function

*y* = log* _{b}*(

*x*)

is the inverse function of the exponential function

*x* =* b ^{y}*

The logarithm of x=1 is the number y we should raise the base b to get 1.

The base b raised to the power of 0 is equal to 1,

*b*^{0} = 1

So base b logarithm of one is zero:

log_{b}(1) = 0

For example, the base 10 logarithm of 1:

Since 10 raised to the power of 0 is 1,

10^{0} = 1

Then the base 10 logarithm of 1 is 0.

log_{10}(1) = 0