Logarithm Calculator

Calculate logarithms with any base.

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3 Logarithm Calculations - Practical Examples

Definition

What is a Logarithm?

A logarithm is the inverse operation of exponentiation. It answers the question: "To what power must we raise the base to get the number?" For example:

Example:

log₂(8) = 3

This means 2 raised to the power of 3 equals 8

Steps

How to Calculate Logarithms

To calculate a logarithm:

1
Identify the base and the number
2
Use the formula: logₐ(b) = x, where a is the base, b is the number, and x is the power
3
Calculate x using the formula: a^x = b

For example, to calculate log₁₀(100):

Example:

10^x = 100
x = 2
log₁₀(100) = 2

Examples

Logarithm Calculations - Practical Examples

Example 1 Common Logarithm

Calculate log₁₀(1000).

10^x = 1000
x = 3
Result: 3

Example 2 Natural Logarithm

Calculate ln(e²).

e^x = e²
x = 2
Result: 2

Example 3 Binary Logarithm

Calculate log₂(16).

2^x = 16
x = 4
Result: 4

Tools

Mathematics Calculators

Logarithm Percentage Percentage Increase Mode Lcd

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