Logarithm Calculator
Calculate a real logarithm in any valid base, or raise that base to an exponent. Compare natural, binary and decimal logarithms and inspect the inverse relationship.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use change of base: divide the natural logarithm of x by the natural logarithm of b. The inverse operation raises b to y. A base between 0 and 1 is valid and produces a decreasing logarithm function.
y = log_b(x) = ln(x)/ln(b); inverse: x = b^y; x>0, b>0, b≠1
Worked example
log₁₀(1000) = 3 because 10³ = 1000. log₂(8) = 3. For base 0.5, log₀.₅(8) = −3 because 0.5⁻³ = 8.
Assumptions and input details
This is a real-number calculator: zero and negative logarithm arguments are rejected. In power mode, enter the exponent in the same value field. Overflow, underflow to zero and results with magnitude above 1e100 are rejected. The graph shows log_b(x) near the positive input or solved value. Reference powers outside the supported result range are labelled rather than breaking an otherwise valid calculation.
References: OpenStax: logarithmic functions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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