# What is a logarithm / What are logarithms

## Logarithms

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:

• ${\log _a}x=y$
• $x=a^{y}$