How this calculation works
A logarithm answers “what power of this base produces the number?” The number and base must be positive, and the base must not be 1.
log_base(number) = ln(number) ÷ ln(base)A worked example
The logarithm of 1,000 to base 10 is 3.
Good to know
Uses the stated formula and assumptions. Displayed decimal values are rounded; use consistent units for all inputs.
Logarithms turn multiplication into addition
In base 10, 100 has logarithm 2 and 1,000 has logarithm 3. Multiplying them gives 100,000, whose logarithm is 5: the exponents add. This property helps explain why logarithms are useful when values span many orders of magnitude.
An equal step on a logarithmic scale represents an equal ratio, not an equal arithmetic difference. Going from 10 to 100 and from 100 to 1,000 both multiplies by 10, even though the differences are 90 and 900.
A valid base is not just any positive number
The base must be positive and different from 1. A base of 1 cannot identify a unique exponent because every power of 1 remains 1. The number whose logarithm is taken must also be positive in a real-valued calculation.
For physical quantities, logarithms usually apply to dimensionless ratios defined by the model. Do not insert a unit-bearing measurement into a logarithm without understanding the reference quantity or normalization.
A few questions, answered
What is log base 10 of 1?
Zero, because 10⁰ = 1.
Can I calculate a natural logarithm?
Use the mathematical constant e as the base, approximately 2.718281828459045. The entered decimal is an approximation.