Overview
A logarithm is the exponent to which a base must be raised to obtain a number: log_b(x) = y means b^y = x. Logarithms turn multiplication into addition and division into subtraction, which makes them useful for exponential equations and logarithmic scales such as decibels and pH.
Formula
log_b(x) = y ⇔ b^y = x, with x > 0, b > 0 and b ≠ 1.
How it works
Enter the number x
It must be positive.
Enter the base b
A positive base different from 1.
Compute the logarithm
The calculator divides ln(x) by ln(b).
Review the relations
The natural, common and exponential check values appear.
Worked examples
Example 1: log₁₀(100)
The result is 2 because 10² = 100.
Example 2: log₂(32)
The result is 5 because 2⁵ = 32.
Frequently asked questions
What is the difference between log and ln?
log commonly means the base-10 logarithm, while ln is the natural logarithm with base e.
Why can't the base be 1?
Because 1 raised to any power equals 1, so other numbers cannot be reached.
Why is the logarithm undefined for negative numbers?
A positive base raised to a real power cannot produce a negative number.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.