Logarithm Calculator Formula
Understand the math behind the logarithm calculator. Each variable explained with a worked example.
Formulas Used
Log10 Val
log10_val = log10(x)Ln Val
ln_val = log(x)Custom Log
custom_log = log(x) / log(base_val)Variables
| Variable | Description | Default |
|---|---|---|
x | Number | 100 |
base_val | Custom Base | 2 |
How It Works
How Logarithms Work
Definition
log_b(x) = y means b^y = x
The logarithm answers: "To what power must I raise the base to get this number?"
Common Types
Change of Base Formula
log_b(x) = ln(x) / ln(b)
Worked Example
Calculate the logarithms of 100.
- 01log₁₀(100) = 2 (because 10² = 100)
- 02ln(100) ≈ 4.605170
- 03log₂(100) = ln(100)/ln(2) ≈ 6.643856
Frequently Asked Questions
What is a logarithm?
A logarithm is the inverse of exponentiation. log_b(x) answers the question: what power of b gives x?
What is the difference between log and ln?
log (or log₁₀) uses base 10 and is common in science and engineering. ln uses base e (≈2.718) and is the natural logarithm used in calculus.
Can you take the log of a negative number?
Not in the real number system. Logarithms are only defined for positive real numbers. The complex logarithm extends this to negative numbers.
Learn More
Guide
Understanding Logarithms - Complete Guide
Learn what logarithms are, how they work, and how to use them. Covers log rules, common and natural logarithms, change of base, and real-world applications.
Ready to run the numbers?
Open Logarithm Calculator