Exponent & Logarithm Calculator

Formula used

bᵉ multiplies b by itself e times. log_b(x) = ln(x) ÷ ln(b), the inverse operation

How to use this calculator

1. Choose exponent or logarithm mode.
2. In exponent mode, enter the base and the power — fractional and negative exponents both work.
3. In logarithm mode, enter the base and the number you want the logarithm of.

Example calculation

What does this result mean?

Exponents and logarithms are inverses: if 2⁵ = 32 then log₂32 = 5. Logarithms compress huge ranges into manageable numbers, which is why they underpin decibels, pH, the Richter scale and algorithmic complexity. A fractional exponent is a root — x^0.5 is the square root of x — and a negative exponent is a reciprocal.

Frequently asked questions

What is a natural logarithm?

A logarithm to base e ≈ 2.71828. It appears throughout calculus and any process with continuous growth or decay.

Why is any number to the power of zero equal to one?

Because bⁿ ÷ bⁿ = b⁰ and any non-zero number divided by itself is 1. Zero to the power zero is left undefined by convention in most contexts.

What does a negative exponent mean?

It is a reciprocal: 2⁻³ = 1 ÷ 2³ = 0.125.

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