Simplify the logarithm log2 (64)

Question

answer choices for correct solution are;

1. 6

2. 64

3. 62

4. 32

Answer 1

Definition: The logarithm of a number, to a particular base, is the power to which the base must be raised to give the given number.

So, let log2 (64)  = x, where the base of the logarithm is 2.

Going by the above definition, log2 (64) is x, so 64 (the given number) must be 2 (the base) to the power x.

i.e. 64 = 2^x

but 64 = 2^6

i.e. 2^6 = 2^x

Therefore, x = 6

Answer: log2 (64) = 6