Logarithm Calculator
Calculate logarithms with any base including natural log (ln) and common log (log10).
A logarithm calculator computes logarithms, antilogarithms, natural logarithms, and change-of-base conversions for any positive number.
Examples
Common log
Natural log
Change of base
Frequently Asked Questions
What is a logarithm?
What is the natural logarithm?
Why can you not take the log of a negative number?
Quick Tips
- •Double-check your inputs — small errors lead to incorrect results.
- •Use the change-of-base formula to convert between logarithm bases.
- •Remember that log base 10 of 1000 is 3, which is a quick sanity check.
A logarithm calculator computes logarithms, antilogarithms, natural logarithms, and change-of-base conversions for any positive number.
How to Use This Calculator
Select the calculation mode: logarithm, antilogarithm, natural log, or change of base. Enter the value and base as needed. The calculator will compute the result and show equivalent representations.
Understanding the Formula
log_b(x) = ln(x)/ln(b); Antilog: b^x; Change of base: log_a(x) = log_b(x)/log_b(a)
Examples
Common log
log₁₀(1000) = 3, because 10³ = 1000
Natural log
ln(e²) = 2, because e² ≈ 7.389
Change of base
log₂(8) = ln(8)/ln(2) = 2.079/0.693 = 3
Frequently Asked Questions
What is a logarithm?
A logarithm answers the question: to what power must the base be raised to get a given number? log_b(x) = y means b^y = x.
What is the natural logarithm?
The natural logarithm (ln) uses base e ≈ 2.71828. It appears naturally in calculus, compound interest, and exponential growth/decay.
Why can you not take the log of a negative number?
In real numbers, logarithms are only defined for positive values because no real power of a positive base produces a negative result.
Assumptions & Limitations
- Assumes positive input values; logarithms of zero or negative numbers are undefined in real numbers.
- Assumes the base is positive and not equal to 1.
- Results may show floating-point approximations for irrational numbers.