Question

Evaluate the following expression. you should do this without a calculator log4 256

Answer 1

4

Explanation:

Using the rule of logarithms

•
`log_(b)` x = n ⇔ x =
`b^(n)`

let
`log_(4)` 256 = n, then

256 =
`4^(n)`

Note that 256 =
`4^(4)`, hence

`4^(4)` =
`4^(n)`

Since the bases are equal ( both 4) equate the exponents, hence

n = 4