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,

b⁰ = 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,

10⁰ = 1

Then the base 10 logarithm of 1 is 0.

log₁₀(1) = 0

See also