Question 1

What is a logarithm?

Accepted Answer

A logarithm answers the question: to what power must the base be raised to get this number? log base b of x = n means b raised to the n equals x. For example log₂ 8 = 3 because 2³ = 8.

Question 2

What are ln and log?

Accepted Answer

ln is the natural logarithm with base e (≈ 2.71828). log without a base usually means log base 10 (common logarithm). This calculator shows both along with log base 2 and any custom base.

Question 3

What is the change-of-base formula?

Accepted Answer

log base b of x equals ln(x) / ln(b), or equivalently log₁₀(x) / log₁₀(b). This lets you compute a logarithm in any base using a calculator that only has ln or log buttons.

Question 4

Can you take the log of a negative number?

Accepted Answer

Not as a real number. The logarithm is only defined for positive inputs when working with real numbers. The log of zero is negative infinity, and the log of a negative number is a complex number.