Base 2 logarithm
log_2(8)3
Log Calculator
Use this free log calculator to find logarithms with any valid base, compare ln and log10 values, check the exponential form, and see change-of-base steps.
Custom bases ln and log10 Change-of-base steps Power check
log_2(8)3
- ln(value)
- 2.0794415417
- log10(value)
- 0.903089987
- Power check
- 8
Steps
- Start with log base 2 of 8.
- Use the change-of-base formula: log_b(x) = ln(x) / ln(b).
- Substitute the values: ln(8) / ln(2) = 2.0794415417 / 0.6931471806.
- The answer is 3.
How to use the Log Calculator
- Enter the positive value you want to evaluate.
- Enter a positive base that is not 1, such as 2, 10, or e.
- Press Calculate log to see the logarithm, ln, log10, power check, and steps.
- Use examples, recent answers, or copy the answer while you study logarithms.
What people use it for
Calculate log base 2, base 10, natural log, or another custom base.
Check logarithm homework with change-of-base steps.
Compare log, ln, and log10 values from one input.
Confirm a logarithm by seeing the matching exponential power check.
Quick examples
Common logarithm
log_10(1000)3
Natural logarithm
ln(e^3)3
Need the guide or a nearby tool?
Need a slower walkthrough, a related calculator, or the full library? These links keep you close to the task you started.
- How to use the Log Calculator See slower examples, input meanings, formula notes, result limits, and mistakes to avoid.
- Calculators Browse related calculators and utilities in the same category.
- Calculator and utility guides Find more guides that use real tool inputs and example numbers.
- All free tools Search every live tool, converter, calculator, AI helper, and browser utility.
Frequently asked questions
Quick answers about valid bases, ln, log10, change-of-base, exponential checks, and privacy.
What formula does the Log Calculator use?
It uses the change-of-base formula: log_b(x) = ln(x) / ln(b). This lets the calculator solve logarithms for any valid positive base except 1.
What values can I enter?
The log value must be greater than zero. The base must also be greater than zero, and the base cannot be 1.
What do the main Log Calculator inputs mean?
The main inputs are the numbers, operation, mode, or known values the calculator needs. Keep units consistent, enter percentages the way the page label shows, and use the examples as a quick check before trusting the answer.
How should I read the Log Calculator answer?
Read the headline answer, then check the supporting lines and examples to understand how the calculator got there. If one input changes, rerun the tool and compare the new answer instead of guessing.
What should I double-check before trusting the Log Calculator?
Check units, signs, rounding, and the selected mode before copying the answer. If the number feels weird, rerun one of the examples first, then put your own values back in slowly.
What is the difference between log, log10, and ln?
log10 means base 10, ln means base e, and a custom log lets you choose another base such as 2, 3, or 5.
How can I check a logarithm answer?
Rewrite it as an exponent. If log base b of x equals y, then b^y should equal x. The calculator shows this check in the result card.
Can logarithm answers be negative?
Yes. A logarithm can be negative when the value is between 0 and 1 for a base greater than 1, such as log_10(0.01) = -2.
Is my log calculation history private?
Yes. Recent log answers stay only in the current browser tab while you use the page. They are not sent to a server.
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