Log Calculator - calculatorsee.com


Log Calculator

Calculate logarithms for any positive base (b) and argument (x), including natural logarithm ln(x) and common base-10 log₁₀(x).

Calculator Inputs

Positive number.
Base (default 10).

Calculated Results

Calculated Logarithm
log₁₀(1000) = 3.000
Natural Logarithm ln(x) 6.9078
Binary Logarithm logâ‚‚(x) 9.9658
Exponential Equivalent 10³ = 1000
Values calculate live as you adjust inputs.

About Log Calculator

A logarithm is the exponent to which a specified base (b) must be raised to produce a given number (x). If bʸ = x, then log_b(x) = y.

What is Log Calculator?

A logarithm is the exponent to which a specified base (b) must be raised to produce a given number (x). If bʸ = x, then log_b(x) = y.

How to Use This Calculator

  1. Enter the positive argument x.
  2. Specify the logarithm base b (use 10 for common, 2.71828 for natural).
  3. View the logarithmic power.

The Mathematical Formula & Variables

log_b(x) = ln(x) / ln(b)

Variables Definition

Symbol / Variable Name Description
ln Natural Log Logarithm with base e (Euler's constant ~2.71828).

Step-by-Step Worked Example

Scenario: Calculate log₁₀(1000).

  1. Since 10 * 10 * 10 = 10³ = 1000, the logarithm is 3.
  2. ln(1000) / ln(10) = 6.907755 / 2.302585 = 3.000.

Result: log₁₀(1000) = 3

Frequently Asked Questions

Can you take the logarithm of a negative number?

In real arithmetic, logarithms of negative numbers and zero are undefined because no real power of a positive base can yield zero or a negative value.