Logarithm Calculator

Solve one part of log_b(x) = y by entering the other two values.

Select value to calculate

The calculator will show only the inputs needed for the selected calculation.

Number (x)

The number inside the logarithm. Must be greater than 0.

Base (b)

The base must be greater than 0 and cannot equal 1.

Logarithm value (y)

The result of the logarithm expression.

Rule: The logarithm equation is log_b(x) = y. Valid logarithms require x > 0, b > 0, and b ≠ 1.

Use this Log Calculator to solve one missing value in the logarithmic equation log_b(x) = y. You can calculate the logarithm value, original number, or base.

Calculation Methods

Logarithmic and exponential forms are equivalent:

log_b(x) = y

b^y = x

To calculate a logarithm with any valid base:

log_b(x) = ln(x) ÷ ln(b)

To find the original number:

x = b^y

Example

Calculate:

log₂(32)

Because:

2⁵ = 32

Therefore:

log₂(32) = 5

Important Note

For real-number logarithms, x must be greater than 0, the base must be greater than 0, and the base cannot equal 1.

Source

OpenStax College Algebra 2e — Logarithmic Properties and Change of Base

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