A logarithm answers: 'To what power must the base be raised to get this number?' log₁₀(1000) = 3 because 10³ = 1000. Logarithms turn multiplication into addition, making them essential for scientific scales (decibels, Richter, pH), compound interest, and algorithm analysis.
How to Use
Enter a number and base:
- Common: log₁₀(x)
- Natural: ln(x) = logₑ(x)
- Binary: log₂(x)
- Custom: Any base
Log Properties
- log(a×b) = log(a) + log(b)
- log(a/b) = log(a) − log(b)
- log(aⁿ) = n × log(a)
- log(1) = 0 for any base
- log_b(b) = 1
Change of Base
log_b(x) = log(x) / log(b) = ln(x) / ln(b). This formula lets you calculate any base logarithm using your calculator's log or ln button.
Step-by-Step Instructions
- 1Enter the number.
- 2Select the logarithm base.
- 3View the result.
- 4Check the antilog (inverse).
- 5Review the change of base calculation.