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Logarithm Calculator

Pick a mode, type the numbers it asks for, and press Calculate to get a logarithm, a change-of-base ratio, or an anti-logarithm. The results appear in cards below the button.

What this calculator does

One form covers three modes. Logarithm returns log_b(x) from a Number (x) and a Base (b). Change of base returns the same logarithm in a New base (c), worked out as the ratio log_c(x) / log_c(b). Anti-logarithm runs the other direction, raising the Base (b) to an Exponent (y) to give bʸ.

Each mode asks for its own fields: the first for a number and a base, the second for a third value, the new base, and the last for a base and an exponent. Nothing is worked out until you press Calculate.

How a logarithm reads

A logarithm answers a power question. When bʸ = x, the base-b logarithm of x is y. That is why a logarithm of 100 to base 10 comes back as Logarithm: 2, and why the reverse step — base 10 raised to the exponent 2 — returns Anti-logarithm: 100.

The other examples on this page follow the same shape: log₂(1024) = 10 and logₑ(e) ≈ 1.

Logarithm formula

log_b(x) = y when bʸ = x.

Change of base: log_b(x) = log_c(x) / log_c(b).

Anti-logarithm: when y = log_b(x), the value behind the logarithm is bʸ.

Using the results

Change of base shows its working, not just an answer. For Number (x) 8, Base (b) 2 and New base (c) 10 the cards report Result: 3 together with log₁₀(8): 0.903089986991944 and log₁₀(2): 0.301029995663981.

Copy writes a result and its unit to the clipboard, so you can drop it straight into your own notes. Clear resets the form. Everything runs in the browser and nothing is uploaded.