Math
Logarithm Calculator
Use this logarithm calculator to answer the question: what power turns the base into the value?
Try an example
Result
Logarithm
—
- Natural log
- —
- Common log
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the logarithm calculator solves
Use this The exponent you would need to raise a base to in order to get a number. calculator to answer the question: what power turns the The number being raised to a power, or the side a shape's height is measured from. into the value?
Formula
How to use it
- Enter the value inside the logarithm.
- Enter the base.
- Use the result as the The small raised number saying how many times to multiply the base by itself. on that base.
How to read the answer
If log_b(x) = y, then b^y = x. That makes logarithms the inverse operation for matching-base exponentials.
Common mistakes and edge cases
- The value must be positive.
- The base must be positive and cannot equal 1.
- Logarithms undo exponentials with the same base.
Worked examples
Common log
Logarithm
2
Base 2 log
Logarithm
5
Frequently asked questions
What is ln?+
ln is the natural logarithm, which uses base e.
What is log base 10?+
It is the common logarithm, often written log(x) in science and calculators. It answers what power of 10 creates the value.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- May 8, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: May 8, 2026