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:
