What is a logarithm / What are logarithms

Logarithms

An old logarithm table and modern calculator
An old logarithm table and modern calculator

Logarithms come in the form {\log _a}x. We say this as 'log to the base a of x. But what does {\log _a}x mean?

Example

1) {\log _5}25 means "What power of 5 gives 25?""

The answer is 2 because {5^2} = 25, in other words {\log _5}25 = 2.

Question

2) {\log _2}16 means, What power of 2 gives 16?

The answer is 4 because {2^4} = 16, in other words {\log _2}16 = 4.

So {\log _a}x means "What power of a gives x?" Note that both a and x must be positive.

You may wish to use these to help remember this:

curriculum-key-fact
  • {\log _a}x=y
  • x=a^{y}