Learning focus 1
Type the number and optionally the base (default: base 10).
Free online calculator
Logarithm Calculator
Evaluate logarithms in any base — common log (base 10), natural log (base e), and arbitrary bases — with change-of-base steps shown.
Step-by-step solutions
Clear, detailed explanations
Instant results
Accurate answers in seconds
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How to Use the Logarithm Calculator
1
Enter the value
Type the number and optionally the base (default: base 10).
2
Apply logarithm rules
We use change-of-base and power rules as needed.
3
Show the result
Get the logarithm value with each step explained.
Example
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What the Logarithm Calculator Helps You Understand
Evaluate logarithms in any base — common log (base 10), natural log (base e), and arbitrary bases — with change-of-base steps shown.
Learning focus 2
We use change-of-base and power rules as needed.
Learning focus 3
Get the logarithm value with each step explained.
Input tips
- • Type the number and optionally the base (default: base 10).
- • log usually means base 10 (common logarithm), while ln means base e (natural logarithm). This calculator supports both.
Common mistakes to avoid
- • Taking a real logarithm of zero or a negative number.
- • Using a logarithm base of 1 or a non-positive base.
Frequently Asked Questions
What is the difference between log and ln?
log usually means base 10 (common logarithm), while ln means base e (natural logarithm). This calculator supports both.
Can I use any base?
Yes. Specify the base as a second argument, e.g. log(8, 2) = 3.