Question

Solve for x: `5^(log x) + 5x^(log 5) =3 (a>0)`
A. `2^("log"_(a)5)`
B. `2^(-"log"_(a)5)`
C. `2^(-"log"_(5)a)`
D. `2^("log"_(5)a)`

Answer 1

Correct Answer - C
We have,
`5^("log"_(a)x) + 5x^("log"_(a)5) = 3`
`rArr x^("log"_(a)5) + 5x^("log"_(a)5) = 3 " " [because x^("log"_(a)y) = y^("log"_(a)x)]`
`rArr 6*x^("log"_(a)5) = 3`
`rArr x^("log"_(a)5) = (1)/(2) rArr x = (2^(-1))^("log"_(5)a) = 2^(-"log"_(5)a)`