Logarithm Calculator
Use this online logarithm calculator to find log base b of x, natural log (ln), common log (log10), and antilog values.
What is a logarithm?
A logarithm answers one simple question: “To what power must we raise a base to get a number?” For example, if 26 = 64, then log2(64) = 6.
In other words, logarithms are the inverse of exponents. That makes them incredibly useful whenever values grow or shrink quickly, such as compound interest, population growth, pH levels, sound intensity, and data scaling.
How to use this logarithms calculator online
1) Choose the calculation type
- logb(x): General logarithm with custom base.
- ln(x): Natural logarithm (base e ≈ 2.71828).
- log10(x): Common logarithm (base 10).
- Antilog bx: Reverse logarithm to recover the original value.
2) Enter your value
Put your number into the Value (x) field. For custom-base logarithms and antilog calculations, also fill in the Base (b) field.
3) Set precision and calculate
Choose the number of decimal places, click Calculate, and the result will display instantly. The tool also shows the exact expression used.
Domain rules (important)
For logarithms to be valid:
- x must be greater than 0.
- b must be greater than 0.
- b cannot equal 1 (for logb(x)).
If an invalid input is entered, the calculator returns a clear error message so you can fix it quickly.
Most useful logarithm formulas
Product rule
logb(MN) = logb(M) + logb(N)
Quotient rule
logb(M/N) = logb(M) − logb(N)
Power rule
logb(Mk) = k · logb(M)
Change of base formula
logb(x) = ln(x) / ln(b) = log10(x) / log10(b).
This is exactly how many calculators compute custom-base logs internally.
Real-world uses of logarithms
- Finance: growth rates, compound return analysis, and doubling time approximations.
- Science: exponential decay, reaction rates, and environmental measurements.
- Engineering: signal processing, decibels, and system dynamics.
- Data science: feature scaling and transforming skewed distributions.
- Education: algebra, pre-calculus, and exam prep with fast verification.
Quick examples
Example A: log2(64)
Since 26 = 64, the answer is 6.
Example B: ln(20)
ln(20) ≈ 2.99573227.
Example C: log10(1000)
Because 103 = 1000, the answer is 3.
Example D: antilog base 10 of 2.5
102.5 ≈ 316.22776602.
Why use an online log base calculator?
A dedicated logarithm calculator helps you avoid manual mistakes, speeds up homework and professional workflows, and gives consistent precision for repeated calculations. Whether you need a quick ln value or a custom base log for technical analysis, this tool covers the essentials in one place.