MulticalcLogarithm Calculator
Calculate ln, log, log₁₀, log₂, and custom basesLogarithm Results
Enter a number to calculate its logarithms.
Logarithm Guide
What is a Logarithm?
A **logarithm** is the inverse operation to exponentiation. If by = x, then logb(x) = y. In other words, the logarithm tells us what exponent we need to raise the base to in order to get a certain number.
Example:
log₁₀(100) = 2 because 10² = 100
Common Logarithm Types
- Natural Log (ln): Base e ≈ 2.71828
- Common Log (log): Base 10
- Binary Log (log₂): Base 2, used in computer science
Logarithm Properties
- log(xy) = log(x) + log(y)
- log(x/y) = log(x) - log(y)
- log(xn) = n·log(x)
- logb(x) = ln(x) / ln(b)
Frequently Asked Questions
No, logarithms are only defined for positive real numbers. log(0) and
log(negative) are undefined in real numbers.
The change of base formula allows you to calculate any logarithm using
natural or common logs: logb(x) = ln(x) / ln(b) or
logb(x) = log₁₀(x) / log₁₀(b).
Quick Tip
Logarithms are widely used in science, engineering, and finance for measuring exponential growth, pH levels, earthquake magnitudes (Richter scale), and sound intensity (decibels).
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Logarithms and Exponentials: