How to Calculate Logarithm
What is Logarithm?
A logarithm answers the question: "To what power must the base be raised to get this number?" log_b(x) = n means bⁿ = x. Logarithms compress enormous ranges and are used in sound (decibels), earthquakes (Richter scale), and pH.
Step-by-Step Guide
- 1log_b(x) = n means bⁿ = x
- 2Common log (log₁₀): log(1000) = 3 because 10³ = 1000
- 3Natural log (ln): ln(e) = 1 because e¹ = e ≈ 2.718
- 4log_b(x) = log(x)/log(b) — change of base formula
Worked Examples
Input
log₁₀(100)
Result
2
10² = 100
Input
log₂(32)
Result
5
2⁵ = 32
Input
ln(e³)
Result
3
Natural log of e³
Input
log₅(125)
Result
3
5³ = 125
Ready to calculate? Try the free Logarithm Calculator
Try it yourself →