Please simplify the expression:

Question

2log(base 4)9 - log(base 2)3

Answer 1

very detailed solution:

let 2log₄ 9 = x
log₄81 = x
4^x = 81
2^(2x) = 81

let log₂ 3 = y
2^y = 3
2^4y = 3^4 = 81

then 2^(2x) = 2^(4y)
---> 2x = 4y
x = 2y

So 2log₄ 9 - log₂ 3
= x - y
= 2y-y
= y
= log₂ 3

Answer 2

log base 4 of 9 + log base 4 of 6