What is a logarithm?

We can explain this by taking a simple power equation such as 2³ = 8 and setting each number as an unknown variable. For instance 2³ = x is solved by cubing 2, x³ = 8 is solved by taking the cube root of 8, whereas 2^x = 8 can't use either of these methods. For this final example we need to introduce the logarithm which is a special function, allowing us to solve the problem. This is defined as log_a(b) = c where a^c = b and a is called the 'base' of the logarithm which is the number raised by a power (2 in my example). Using this gives log₂(2^x) = log₂(8) as every operation must be applied to both sides of the equation. From before we can see log₂(2^x) = x therefore leaving us with x = log₂(8) which can be solved easily by pressing the correct button on your calculator.