How to Calculate Logarithms

How to calculate the base b logarithm of a number x:

log_b x = ?

For example, let's calculate the base 2 logarithm of 90:

log₂ 90 = ?

Most calculators have base 10 and base e only.

Using the logarithm base change rule:

log_b(x) = log_c(x) / log_c(b)

We can change log₂ 90 from base 2 to base 10 and calculate log₁₀ 90 and log₁₀ 2 on the calculator:

log₂ 90 = log₁₀ 90 / log₁₀ 2 = 1.954243 / 0.301030 = 6.491853

See also