Free · Exponents and logarithms
Natural Logarithm & Exponential Inverse
Calculate the real natural logarithm of a positive number or recover the number from its logarithm.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
Loading calculator…
How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
The natural logarithm of 1 is 0. A natural logarithm of 2 corresponds to e², approximately 7.389056.
y = ln(x); x = eʸ
Worked example
Enter these known values and leave the other values blank.
- Positive number x
- 1
- Natural logarithm ln(x)
- 0
Assumptions and limitations
- The real natural logarithm requires a positive input. Zero and negative numbers have no finite real natural logarithm.
- Natural logarithms use base e. Results use finite working precision and are rounded for display.
Common questions
Why is ln(1) zero?
Because e raised to the power zero equals 1.
Is ln the same as log base 10?
No. ln has base e. A base-10 logarithm answers a different exponent question.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.
Related calculators
Explore exponents and logarithms or browse all math calculators.