Work out change of base logarithm instantly with clear inputs, formula shown and shareable results.
Calculators usually offer only ln and log₁₀, so any other base is reached by the change of base rule log_b x = ln x / ln b. The same ratio works with logarithms to any common base.
Change of base
log_b x = ln x / ln b = log₁₀ x / log₁₀ b
ln 100 / ln 5 ≈ 4.6051702 / 1.6094379 ≈ 2.8613531.
Because ln 1 = 0, so the formula divides by zero — and 1 raised to any power is always 1, so the logarithm cannot be defined.