Logarithm — Definition and Evaluation

A logarithm answers the question: to what power must I raise the base to get a given number? We read log₂ 8 as “log base 2 of 8”. Since 2³ = 8, log₂ 8 = 3. So a logarithm is an exponent.

What does this generator do?

On the easy level you evaluate logarithms that come out as whole numbers, for example log₃ 81 or log₂ (1/8). On the medium level you solve equations like log₂ x = 5 and evaluate logarithms with a fractional result, for example log₄ 8 = 3/2. On the hard level you find an unknown base and evaluate expressions like 2^(log₂ 5) and a logarithm of a logarithm.

How to use it

1) Rewrite the logarithm as a power: log_a b = c means a^c = b. 2) Write b as a power of the base a (8 = 2³, 1/9 = 3⁻², √2 = 2^½). 3) Read off the exponent. 4) For an unknown base, solve x^c = b and remember that the base must be positive and not equal to 1.