Question

Find the logarithm of 64 to the base 2√2.​

Answer 1

Solution :

Write 64 as in terms of 2√2.

64 = 26

64 = 24+2

64 = 24 ⋅ 22

64 = 24 ⋅ [(√2)2]2

64 = 24 ⋅ (√2)4

64 = (2√2)4

Then,

log2√264 = log2√2(2√2)4

log2√264 = 4log2√2(2√2)

log2√264 = 4(1)

log2√264 = 4