Log Calculator (Logarithm)
Use our log calculator to compute logarithms with any base. Includes what logarithms are, logarithm meaning, logarithm formula, logarithm properties, examples like logarithm of 1, and how to use log calculator tools (including logarithm on calculator tips).
What are Logarithms?
A logarithm answers the question: “What exponent do I raise a base to, to get a number?” That’s the core of how logarithm works.
In math, the logarithm meaning is tied to exponentiation. If b^y = x, then log_b(x) = y. This idea powers logarithm math topics like logarithmic functions, logarithmic equations, and logarithmic graphs.
Logarithms are used because they turn multiplication into addition and make very large or very small values easier to work with—this is why we use logarithms in science, finance, and computing (including logarithmic scale and logarithmic graph interpretations).
Logarithm Formula
To calculate a logarithm, you’re solving for the exponent y in b^y = x.
x must be > 0, b must be > 0 and b ≠ 1.
Because b^0 = 1 for any valid base b.
Natural log is the logarithm with base e.
How to Use the Log Calculator
- 1
Enter the number x (the value you want the logarithm of).
- 2
Enter the base b (for example 10 for common log, or e for natural log).
- 3
The log calculator computes y = log_b(x).
- 4
If you’re doing logarithm on calculator, use the LOG key for base 10, LN for base e, or the change-of-base method for other bases.
Frequently Asked Questions
A logarithm tells you the exponent needed to raise a base to get a number. If b^y = x, then log_b(x) = y.
Enter x (number) and b (base). The result is log_b(x).
It reverses exponentiation: it solves for the exponent y in b^y = x.
log_b(x) = y ⇔ b^y = x.
It means “the exponent.” log_b(x) is the exponent you apply to base b to get x.
Common properties include: log_b(xy)=log_b(x)+log_b(y), log_b(x/y)=log_b(x)-log_b(y), and log_b(x^k)=k·log_b(x).
They simplify multiplication/division into addition/subtraction, help solve exponential equations, and make large scales easier to interpret (logarithmic scale).
Most calculators provide LOG (base 10) and LN (base e). For other bases, use change of base: log_b(x)=ln(x)/ln(b).
Before calculators, people used logarithm tables to look up log values. Today, a logarithm calculator replaces the need for a logarithm table.
A logarithmic function is y = log_b(x). Its logarithmic graph grows slowly and is defined only for x > 0.
A logarithmic scale is a scale where equal distances represent equal ratios (multiplicative steps), commonly used for sound (decibels), earthquakes, and data spanning many magnitudes.
It’s a calculus technique where you take ln of both sides to simplify derivatives of products/powers—often used in logarithmic differentiation problems.
Yes—logarithms are commonly used to solve logarithmic equations by converting between log form and exponential form.
Real logarithms are only defined for x > 0. If x ≤ 0, the logarithm is not a real number.