Logarithm Calculator
A logarithm answers the question: to what exponent must a given base be raised to produce a certain number? Written as log_b(x) = y, it means b^y = x. This calculator computes the logarithm of any positive number x for any valid base b (where b > 0 and b ≠ 1), including the common presets: base-10 (log₁₀), natural logarithm (ln, base e ≈ 2.718), and binary logarithm (log₂).
The change-of-base formula is the key to computing any logarithm using natural or common logs: log_b(x) = ln(x) / ln(b). This calculator displays the full step-by-step breakdown using this identity, making it easy to verify results and understand the underlying math.
How it works
log_b(x) = ln(x) / ln(b) = log(x) / log(b). Special cases: log₁₀(x) = log(x), ln(x) = log_e(x), log₂(x) = ln(x) / ln(2). Domain: x > 0, b > 0, b ≠ 1.
Use cases
- Solving exponential equations in algebra and pre-calculus
- Calculating decibel levels in acoustics and signal processing
- Computing pH values in chemistry (pH = −log₁₀[H⁺])
- Analyzing algorithm complexity in computer science (e.g., O(log n))
- Measuring earthquake magnitudes on the Richter scale