Logarithm Calculator
Solve Logarithm step by step — enter coefficients or expressions to get roots, factors, or simplified forms with detailed algebraic working.
Formula
y = log_b(x)
Finds the exponent y such that b^y = x.
Worked Examples
Example 1: Log Base 10
Problem:log10(100)
Solution:10^2 = 100
Result:2
Example 2: Log Base 2
Problem:log2(8)
Solution:2^3 = 8
Result:3
Example 3: Natural Log
Problem:ln(e)
Solution:e^1 = e
Result:1
Frequently Asked Questions
What is a logarithm?
A logarithm is the inverse operation to exponentiation. It answers the question: "To what power must I raise the base b to get x?"
Can you take the log of a negative number?
No. In the real number system, you cannot take the logarithm of a negative number or zero. The domain of log(x) is x > 0.
Who invented logarithms?
John Napier introduced logarithms in the early 17th century to simplify complex calculations in astronomy and navigation.
Background & Theory
**Logarithm:**
The inverse function to exponentiation.
**log_b(x) = y ⟺ b^y = x**
**Common Bases:**
* **Common Log:** Base 10 (log x). Used in science/engineering.
* **Natural Log:** Base e (ln x). Used in math/physics. e ≈ 2.718.
* **Binary Log:** Base 2 (lg x). Used in computer science.
**Properties:**
* log(ab) = log(a) + log(b)
* log(a/b) = log(a) - log(b)
* log(a^n) = n·log(a)
History
Logarithms were introduced by John Napier in 1614 as a means to simplify calculations. By turning multiplication into addition, they revolutionized navigation, astronomy, and engineering for centuries until electronic calculators were invented.