log8 4(square root sign) 1/2

Answer 1

log₈ 4√(1/2)

recall that log_aa^k = k

so we have to change 4√(1/2) to base 8

4√(1/2)
= 4/√2
= 4/√2 (√2/√2)
= 2√2
= (8^(1/3)) (8^(1/6))
= 8^(1/2)

so log₈ 4√(1/2)
= log₈ 8^(1/2)
= 1/2