Math
Logarithm Calculator
Use this logarithm calculator to answer the question: what power turns the base into the value?
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 logarithm calculator to answer the question: what power turns the base into the value?
Formula
How to use it
- Enter the value inside the logarithm.
- Enter the base.
- Use the result as the exponent 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.
Related calculators
Exponent Calculator
Calculate powers with positive, negative, and decimal exponents while showing the exponent rule used.
Scientific Notation Calculator
Convert regular numbers to scientific notation and show coefficient, exponent, and engineering notation.
Square Root Calculator
Calculate square roots, simplify exact radicals for whole numbers, and identify perfect squares.
Discount Calculator
Calculate sale price, stacked discounts, original price before a discount, or the discount percent between two prices.
Fraction Calculator
Add, subtract, multiply, divide, simplify, compare, or convert decimals to fractions with steps and visual fraction bars.
Percentage Calculator
Calculate percent of a number, part-to-whole percentages, percent change, missing wholes, and reverse percent changes.
Last updated: May 8, 2026