How to Use the Logarithm Calculator
This calculator computes logarithms in any base and converts between ln, log₁₀, and log₂ simultaneously. It also handles inverse logarithm (antilog) calculations. Ideal for math, science, and engineering work.
Change-of-Base Formula
log_b(x) = ln(x) / ln(b) = log₁₀(x) / log₁₀(b). This formula converts any logarithm into natural or common log form, which is what this calculator uses internally for all base conversions.
Antilog
The antilog reverses a logarithm. If log_b(x) = y, then b^y = x. In antilog mode, enter the base and exponent to find the original value. For example, antilog₁₀(3) = 10³ = 1000.
Input Rules
Base b must be positive and not equal to 1 (b > 0, b ≠ 1). Argument x must be positive (x > 0). The exponent in antilog mode can be any real number.
Frequently Asked Questions
Use ln (natural log) in calculus, physics, and growth/decay problems. Use log₁₀ (common log) for pH, decibels, and general engineering calculations.
Yes. If 0 < x < 1, then log_b(x) is negative for b > 1. For example, log₁₀(0.01) = -2.
1^y = 1 for any y, so log₁(x) would have no solution for x ≠ 1 and infinitely many solutions for x = 1. It is undefined in standard mathematics.