Question

If `"log"_(3) x + "log"_(9)x^(2) + "log"_(27)x^(3) = 9`, then x =
A. 3
B. 9
C. 27
D. none of these

Answer 1

Correct Answer - C
We have,
`"log"_(3)x + "log"_(9)x^(2) + "log"_(27)x^(3) = 9`
`rArr "log"_(3) x + "log"_(3^(2)) x^(2) + "log"_(3^(3)) x^(3) = 9`
`rArr "log"_(3) x + (2)/(2) "log"_(3) x + (3)/(3) "log"_(3)x =9`
`rArr 3 "log"_(3) x = 9 rArr "log"_(3) x = 3 rArr x = 3^(3)=27`