I don't understand how log2 √(1/2) turned into log2 2^(-1/2).

Question

Quote:
You will have to know the 3 prime properties of logs

1. logk (AB) = logk A + logk B
2. logk(A/B) = logk A - logk B
3. logk (A^n) = n logk A
where k is any positive number , k ≠ 1

so log2√36 - log2 log2</sub√72
= log2 (√36/√72)
= log2 √(36/72)
= log2 √(1/2)
= log2 2^(-1/2)
= (-1/2) log2 2
= (-1/2)(1)
= -1/2

Answer 1

Review the laws of exponents

First of all √2 = 2^(1/2)
then
√(1/2)
= √1/√2
= 1/√2 = 1/2^(1/2) = 2^(-1/2)

based on 1/a^n = a^-n