Asked by Alisha
Please simplify the expression:
2log(base 4)9 - log(base 2)3
2log(base 4)9 - log(base 2)3
Answers
Answered by
Reiny
very detailed solution:
let 2log<sub>4</sub> 9 = x
log<sub>4</sub>81 = x
4^x = 81
2^(2x) = 81
let log<sub>2</sub> 3 = y
2^y = 3
2^4y = 3^4 = 81
then 2^(2x) = 2^(4y)
---> 2x = 4y
x = 2y
So 2log<sub>4</sub> 9 - log<sub>2</sub> 3
= x - y
= 2y-y
= y
= log<sub>2</sub> 3
let 2log<sub>4</sub> 9 = x
log<sub>4</sub>81 = x
4^x = 81
2^(2x) = 81
let log<sub>2</sub> 3 = y
2^y = 3
2^4y = 3^4 = 81
then 2^(2x) = 2^(4y)
---> 2x = 4y
x = 2y
So 2log<sub>4</sub> 9 - log<sub>2</sub> 3
= x - y
= 2y-y
= y
= log<sub>2</sub> 3
Answered by
Anonymous
log base 4 of 9 + log base 4 of 6
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