Common log
Input
- x: 1000
- Base: 10
Calculation
10^3 = 1000
Result
log10(1000) = 3.
Logarithm Calculator
Compute logarithms and solve exponential relationships.
- Formula-based results
- Worked examples included
- Mobile-friendly layout
- Clear input labels
Compute logarithms and solve exponential relationships.
Overview
Logarithms are inverse operations of exponentiation and describe how many times a base must be multiplied to reach a value. They are used in pH scales, signal processing, and growth analysis.
Common logarithms use base 10, natural logarithms use base e, and other bases appear in computing and information theory. A log calculator helps verify transforms and solve equations quickly.
Understanding domain rules is essential: logarithms require positive arguments and valid positive bases not equal to one. This tool enforces those constraints and provides consistent numeric output.
Steps
Select base 10, base e, or a custom positive base.
Provide a positive argument value x.
The tool evaluates y where b^y = x.
Convert between bases when needed for verification.
Rearrange exponential models and solve unknown exponents.
Math
log_b(x) = ln(x) / ln(b), with x > 0, b > 0, b != 1
Change-of-base converts any logarithm into a ratio of natural logs. This makes computation consistent across calculator implementations.
Worked cases
10^3 = 1000
log10(1000) = 3.
ln(e^2) = 2
Result = 2.
2^6 = 64
log2(64) = 6.
Why use this
Questions