About Log Base 10 Calculator
This log base 10 calculator finds the power of 10 that gives your number. Powers of ten give whole-number answers: log10(1000) = 3 and log10(0.001) = -3. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The page opens on log10(2500), about 3.39794000867. The whole part, 3, says the number is in the thousands, and the decimal part comes from its leading digits. That is how slide rules and log tables worked.
Common logs appear in the pH scale, in decibels, in the Richter scale and in scientific notation: the exponent of 10 in scientific notation is the floor of the log10.
How to use Log Base 10 Calculator
- Choose a mode: log of any base, ln, log10, log2, antilog or solve b^x = y.
- Enter the base (not needed for ln, log10 and log2) and the number. You can type fractions like 1/8, powers like 2^10 or the constant e.
- Read the exact or decimal answer at the top.
- Open the steps for the definition, the change of base and, when the number is an integer, the product and power rules applied to its prime factors.
- For an exponential equation such as 1.05^x = 2, choose Solve b^x = y.
Features
- Log of any base, with exact rational answers when the number is an exact power of the base.
- Natural log, common log and binary log as one-click modes.
- Antilogarithm: b raised to the power y, exact for integer exponents.
- Solve b^x = y, the form of compound interest, growth and half-life questions.
- Change-of-base steps using both ln and log10.
- Product and power rules shown on the prime factors of an integer argument.
- Related logs in bases e, 10 and 2, and a list of the logarithm rules.
- Plain explanations of domain errors.
Common logarithm
The common log counts powers of ten.
log10(10^n) = n
log10(a × 10^n) = n + log10(a)Worked examples
log10 2500 gives ≈ 3.39794000867
2500 = 2.5 × 10³, so the result is 3 + log10(2.5).
log10 0.001 gives -3
10^-3 = 0.001.
Privacy: how it works
- Everything is calculated by code running in your browser tab. The numbers you enter are not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- To check a log, raise the base to your answer. It should give back the number.
- log of a number between 0 and 1 is negative, and log of 1 is 0 in every base.
- For doubling time at a rate r per period, solve (1 + r)^x = 2 with the Solve mode.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What does log10 mean?
log10(x) is the power you raise 10 to in order to get x. It is often written simply as log in school mathematics.
How is log10 used for pH?
pH is the negative log10 of the hydrogen ion concentration, so a concentration of 10^-7 gives pH 7.
More Logarithm Calculator pages
- Logarithm CalculatorPick the logarithm you need, enter the base and the number, and get the answer with the change-of-base working.
- Natural Log CalculatorEnter a positive number to get ln(x), the logarithm to base e.
- Log Base 2 CalculatorEnter a positive number to get log2(x), how many times you can halve it.
- Antilog CalculatorEnter a base and an exponent to get the antilogarithm, b raised to y.
- Change of Base CalculatorEnter a base and a number to see log_b(x) worked out with the change-of-base formula.
- Solve Exponential EquationsEnter a base b and a target y to solve b^x = y for x.