What This Calculator Does

The Logarithm Calculator answers two inverse questions:

• Given a base b and value x, find the exponent log_b(x).
• Given a base b and exponent y, evaluate the power b^y.

The page has a Logarithm mode and a Power mode. Logarithm mode shows the custom-base result, reference values for ln(x) and log10(x), and the relationship b^y=x so you can check the setup. It is useful for classwork, homework checks, change-of-base calculations, and basic exponential-growth verification.

If you need parentheses, functions, or several operators in one formula, use the Mathematical Expression Calculator. For a keypad workflow with trig, ln, log, and exponent keys, use the Scientific Calculator. For reporting a result to a chosen number of decimal places, use the Rounding Calculator.

When to Use It

• You need log_2(32), log_10(0.01), or log_3(10).
• You want a valid custom base rather than only base 10 or base e.
• You want to compute a power and then verify the exponent with a logarithm.
• You want to compare a custom-base logarithm with the natural and common logarithms of the same value.

This is not an equation solver, logarithm simplifier, or complex-number calculator. It expects one base and one value or exponent at a time.

Inputs Explained

Mode