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If 3^x=4^(x-1) , then x=...

If `3^x=4^(x-1)` , then `x=`

A

` (2 log_(3) 2)/(2log_(3) 2-1)`

B

` 2/(2-log_(2)3)`

C

` 1/(1-log_(4)3)`

D

` (2 log_(2)3)/(2 log_(2) 3-1)`

Text Solution

Verified by Experts

` 3^(x) = 4^(x- 1)`
` rArr log_(2) 3^(x) = ( x- 1) log_(2) 4 = 2 (x-1)`
` or x log_(2) 3 = 2 x - 2`
` or x = 2/(2-log_(2) 3)`
Rearranging, we get
` x = 2/(2-2/(log_(3)2))=(2 log_(3)2)/(2 log_(3) 2-1)`
Rearranging again, we get
` x = (log_(3)4)/(log_(3)4-1) =(1/(log_(4)3))/(1/(log_(4)3)-1)=1/(1-log_(4)3)`.
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