Logarithm Calculator 2025: Complete Guide
Master logarithms in seconds. Our Log Calculator evaluates, simplifies, changes bases, and solves log equations with full step-by-step explanations.
The 6 Core Log Properties
1. Product: log_b(mn) = log_b(m) + log_b(n)
2. Quotient: log_b(m/n) = log_b(m) - log_b(n)
3. Power: log_b(m^k) = k·log_b(m)
4. Change of Base: log_b(a) = ln(a)/ln(b)
5. log_b(b) = 1, log_b(1) = 0
6. ln(e^x) = x
Step-by-Step: Solve log₂(8)
- 8 = 2³
- log₂(2³) = 3·log₂(2) = 3·1 = 3
Solve log(x) + log(x-1) = log(12)
- log[x(x-1)] = log(12)
- x² - x = 12
- x² - x - 12 = 0
- x = [1±√49]/2 → x = 4 (discard negative)
Real-World Uses
- pH = -log[H⁺]
- dB = 10log(P/P₀)
- Richter = log(I/I₀)
- Half-life: t = ln(2)/k
FAQs
What is ln? Natural log (base e ≈ 2.718).
Can I solve log equations? Yes — type log(x)=2.
Conclusion
From chemistry to finance, logs are everywhere. Use our 2025 Logarithm Calculator for instant, accurate, step-by-step solutions. Try it now!