A walkthrough, end to end.
- 1
Enter the value (must be positive) and the logarithm base.
- 2
The calculator returns log_base(value) — using the change-of-base formula internally.
- 3
Common bases (10, e, 2) have buttons; custom bases supported.
Logarithm definition
log_b(x) = y means b^y = x. Inverse of exponentiation. Change-of-base formula: log_b(x) = log(x) / log(b) — the calculator uses this internally to handle any base.
What you can do with this.
log₁₀ — orders of magnitude
log₁₀(1000) = 3. log₁₀(10⁶) = 6. Useful for understanding large-number scale: pH, decibels, Richter scale, financial growth.
Natural log (ln, base e)
ln(x) is logarithm base e (≈ 2.71828). Foundation of exponential growth/decay equations, continuous compounding, calculus.
log₂ — binary / computer science
log₂(1024) = 10. Used in algorithm complexity (O(log n) is base 2), information theory (bits = log₂ of states), audio engineering.
pH calculation
pH = −log₁₀([H⁺]). Higher pH = lower hydrogen concentration. The calculator computes log₁₀ for pH given hydrogen ion concentration.
Richter scale
Each whole-number step is 10× the amplitude (log₁₀ scale). Magnitude 7.0 quake is 10× stronger amplitude than 6.0 — and ~32× stronger energy release.
Decibel calculation
dB = 10 × log₁₀(P/P₀). Sound intensity ratio expressed logarithmically. Useful for any signal-to-noise or loudness comparison.
Compound interest doubling time
Doubling time ≈ ln(2) / r where r is the periodic rate. The calculator's ln gives 0.693, so for 7% annual rate: 0.693/0.07 ≈ 9.9 years to double.
Log calculator 2026 — what's current
Built into every device. Standalone calculator wins for speed and avoiding mode confusion (some calculators default to natural log; others to log₁₀).
Frequently asked.
Logarithm is only defined for positive real numbers. log of zero is −∞; log of negative numbers is complex (involves imaginary i). The calculator returns error for non-positive inputs.
log usually means log₁₀ (base 10) in non-math contexts. ln always means natural log (base e). Math contexts may use log to mean ln. Always check which is meant.
log_b(x) = log_a(x) / log_a(b) for any common base a. Allows computing any-base log when your calculator only supports specific bases (typically 10 and e).
No. Calculations run entirely in your browser.