How to use the logarithm calculator
Start with the number whose exponent you need. Enter it under Value (x), choose a base in Base (b), and click Calculate. The result area then lists the logarithm, the change-of-base steps, and a power check.
- Enter the number whose logarithm you need in Value (x).
- Enter the base in Base (b), or leave it blank for the natural logarithm.
- Click Calculate to show the result, formula, intermediate values, and check.
- Click Copy result or Download result (.txt) after the result appears.
- Click Reset to clear both fields and hide the result.
How the logarithm formula is calculated
The calculator uses the change-of-base formula log_b(x) = ln(x) / ln(b). It shows the entered value and base, calculates ln(x) and ln(b), divides them, and raises the base to the result for a check. The displayed numbers are rounded.
Value (x): 1000
Base (b): 10
Result: log_10(1000) = 3
Check: 10^3 ≈ 1000For this example, the steps list also shows ln(1000), ln(10), and their division. The final check raises 10 to the calculated result and displays the value it gets.
What values can the logarithm calculator accept?
Value (x) must be finite, positive, and at least 1e-15. Its absolute value cannot exceed 1e15. Zero, negative numbers, blank input, invalid numbers, and values outside these limits produce an error.
Base (b) may be blank or e; either choice uses Euler's number for a natural logarithm. A typed base must be finite and positive, cannot equal 1, and cannot exceed 1e15 in absolute value. Enter 10 for a common logarithm or 2 for a binary logarithm.
How to calculate a natural logarithm (ln)
Leave Base (b) blank or type e. Enter a positive number in Value (x), then click Calculate. The result uses e as its base and labels it that way. If you edit either input, the page hides the previous result until you calculate again.
When to use another math calculator
Use this calculator for one logarithm with a chosen base. For a base raised to an exponent, use the Exponent Calculator. For equations with variables, use the Algebra Calculator. For an expression that combines logarithms with other operations, use the Scientific Calculator. The Math Calculators page lists the other calculation types.
The calculation runs in the browser using the Value (x) and Base (b) you enter. This page's calculator script makes no network request with those entries. Copy result puts the plain-text result on the clipboard when clipboard access works. If copying fails, the page reveals the text so you can select it manually. Download result (.txt) creates a text file from the same result.
Frequently asked questions
What is the formula for calculating a logarithm?
The formula is log_b(x) = ln(x) / ln(b). The calculator shows both natural logarithms, their division, and a power check using the entered base.
What value and base can I enter?
Value (x) must be finite, positive, and at least 1e-15 with an absolute value no greater than 1e15. A typed Base (b) must be positive, finite, no greater than 1e15 in absolute value, and different from 1.
How do I calculate log base 10?
Enter the number in Value (x), type 10 in Base (b), and click Calculate. For example, log_10(1000) returns 3.
How do I calculate a natural logarithm?
Leave Base (b) blank or enter e, then click Calculate. The calculator uses Euler's number as the base.
Why does the logarithm calculator reject zero or a negative value?
Real logarithms require a positive value, so Value (x) cannot be zero or negative. The calculator shows an error and hides the result for those inputs.