Change the base – If 9^x = 27⁵, what is x?

Some questions will require changing the base of a number with an exponent. For example,

16^x = 256⁴, then what is x?

256 = 16² , meaning that the original equation can be rewritten as 16^x = (16²)⁴ = 16⁸

This will usually involve numbers whose square or cube roots are simple integers.

So it’s useful to get familiar recognizing the first few numbers in these exponent sequences: