Log Calculator
Quickly find your Logarithm result with our free Log Calculator. Simple, fast, and accurate.
Logarithm
Result
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What is a Log Calculator?
A log calculator computes logarithms in any base. It helps solve exponential equations by finding the exponent needed to produce a given number from a specified base.
How to calculate logarithms manually (the formula)
logb(x) = y means by = x. For example, log10(1000) = 3 because 103 = 1000. The change-of-base formula: logb(x) = log(x) / log(b).
Example calculation
log10(1000) = ? 10? = 1000. Since 103 = 1000, log10(1000) = 3. ln(1000) = loge(1000) ≈ 6.908.
Common mistakes
- Taking log of zero or negative numbers — Logarithms are only defined for positive arguments.
- Confusing log and ln — log is base 10; ln is base e (natural log). They give different results for the same input.
- Forgetting the change-of-base formula — Most calculators only have log and ln buttons. Use logb(x) = ln(x) / ln(b) for other bases.
Frequently asked questions
What is a logarithm?
To what power must the base be raised to get x?
What is the difference between log and ln?
log is base 10; ln is base e.
How do I calculate log in any base?
Use logb(x) = log(x) / log(b).
What is the log of 0?
Undefined. Only positive numbers have logarithms.
What is the log of 1?
0 in any base.
What are logarithms used for?
Exponential relationships, pH, decibels, and more.