Expanding Logarithms Calculator

This tool applies the product, quotient and power rules to a logarithm and shows each rewrite as it happens. Enter an expression such as log(x^3*y/z^2), ln(x*sqrt(y)) or log_2(8x^5) and it returns the expanded form together with the rule used at every step, evaluating any logarithm of a number that comes out whole. A second action runs the other way, folding a sum like 3log(x) + 2log(y) - log(z) back into a single logarithm. It reads numbers, single letter variables, multiplication, division, powers with rational exponents and square or cube roots; sums inside the argument, nested logarithms and symbolic exponents are reported rather than guessed at, because no rule expands them.

Calculator Type
Write the whole logarithm, as in log(x^3*y/z^2), ln(x*sqrt(y)) or log_2(8*x^5). Use * for multiplication and ^ for a power.
Only used when the expression itself does not say. A base written into the expression always wins.
Widget
Every term must be a logarithm in the same base, with an optional number in front. A plain number is folded in when base^number is a whole number.
Widget
Related Tools
Log Calculator Simplify Calculator Exponential Function Calculator