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

Options

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)`

Explanation

` 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)`.