Advanced math calculator

Log Calculator

Evaluate y = logᵦ(x), or reverse the relationship to calculate x = bʸ.

Enter values and select Calculate.

Formula and methodology

For a positive base b other than 1, logᵦ(x) = ln(x) / ln(b). Reverse mode uses x = bʸ. This calculator works with real logarithms only.

Worked example

log₁₀(1000) = 3, log₂(32) = 5, ln(e) = 1, and log₃(81) = 4.

Assumptions and boundaries

The logarithm input x must be greater than 0.
The base must be greater than 0 and cannot equal 1.
Reverse results must remain within the browser’s finite numeric range.
Exponent Calculator retains general power-calculation intent.

Inputs and results stay in this browser and are not sent to analytics.