Logarithm Calculator
Calculate Logarithm (logb(x))
About Logarithm Calculator
What Is a Logarithm?
A logarithm answers the question: what exponent do I need to raise the base to in order to get this number? If 2^3 = 8, then log base 2 of 8 = 3. Logarithms are the inverse of exponentiation. They compress enormous ranges into manageable scales, which is why they appear in measuring earthquakes (Richter scale), sound (decibels), acidity (pH), and information (bits). The two most common bases are 10 (common logarithm, written log) and e (natural logarithm, written ln), where e is approximately 2.71828.
Logarithm Rules
Key properties: log(a x b) = log(a) + log(b), log(a/b) = log(a) - log(b), log(a^n) = n x log(a), log(1) = 0, log_b(b) = 1. The change of base formula allows converting between bases: log_b(x) = ln(x) / ln(b).
How to Use This Calculator
Enter the number you want to find the logarithm of and select the base (natural, common, or custom). Click Calculate to see the result. The calculator also provides the antilog (inverse): given a log value and base, it computes the original number. Switch between log and antilog modes using the toggle.
Frequently Asked Questions
What is the difference between log and ln?
Log typically means base-10 logarithm. Ln means natural logarithm (base e = 2.71828). They are related by a constant factor: ln(x) = log(x) x 2.303.
Can you take the log of a negative number?
Not in real numbers. The logarithm of zero and negative numbers is undefined in the real number system. In complex numbers, it involves imaginary components.
What is an antilog?
The antilog reverses a logarithm. If log(x) = y, then antilog(y) = x = 10^y. For natural log, antiln(y) = e^y. It converts from log scale back to the original value.
Related Tools
