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If log4A = log6B = log9(A+B) then the va...

If `log_4A = log_6B = log_9(A+B)` then the value of `B/A` is

A

`(sqrt(5)-1)/(4)`

B

`(sqrt(5)+1)/(4)`

C

`(sqrt(5)-1)/(2)`

D

`(sqrt(5)+1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `log_(4)A=log_(6)B=log_(9)(A+B)=x`
`rArr A=4^(x),B=6^(x)` and `A+B=9^(x)`
`rArr 4^(x)+6^(x)=9^(x)`
`rArr 2^(2x)+2^(x).3^(x)=3^(2x)`
`rArr (3//2)^(2x)-(3//2)^(x)-1=0`
`rArr ((3)/(2))^(x)=(B)/(A)=(sqrt(5)+1)/(2)`
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