If `3^x = 4^(x-1)` then x can not be equal to

Options

A. `(2"log"_(3)2)/(2"log"_(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)`

Answer

D

Explanation

We have,
`3^(x) = 4^(x-1)`
`rArr x "log"_(10) 3 = (x-1)"log"_(10)4`
`rArr x = (x-1) "log"_(3)4`
`rArr x = 2(x-1) "log"_(3)2`
`rArr x (2"log"_(3) 2-1) = 2"log"_(3)2`
`rArr x = (2"log"_(3)2)/(2"log"_(3) 2-1)`
Now, `x = (2"log"_(3)2)/(2"log"_(3) 2-1)`
`rArr x = (2)/(2-(1)/("log"_(3)2)) = (2)/(2-"log"_(2)3)`
`rArr x = (1)/(1-(1)/(2) "log"_(2)3) = (1)/(1-"log"_(2^(2))3) = (1)/(1-"log"_(4)3)`
Hence, option (a), (b) and (c) are correct and option (d) is not correct.