What a logarithm asks
A logarithm answers the question: what power do I raise the base to, to get this number? The base 10 log of 1000 is 3, because 10 cubed is 1000.
Changing the base changes the answer but not the number. The natural log uses base e, about 2.718281828.
Worked example
The log base 10 of 1000 is 3, and the natural log of 1000 is 6.907755.
The check row raises the base back to the answer: 10 to the power 3 is 1000, which confirms the result.
Rules worth knowing
Multiplying inside a logarithm adds outside it: log(ab) = log(a) + log(b). Dividing subtracts.
A power inside becomes a multiplier outside: log(a^n) = n log(a). These rules are why logarithms turn multiplication into addition.
Inputs for the log calculator
Number
The number to take the logarithm of. It must be above zero.
Base
The base of the logarithm. Base 10 is the log key and base e is the natural log. It cannot be 1.
CALCULATOR QUESTIONS
Log calculator questions
What is log base 10 of 1000?
3, because 10 cubed is 1000.
What is the natural log?
The logarithm to base e, about 2.718281828. The natural log of 1000 is 6.907755.
Why can't I take the log of a negative number?
A positive base raised to any power stays positive, so no power gives a negative result.
Why can't the base be 1?
Every power of 1 is 1, so a base of 1 could never describe any other number.