Question

Statement-1: If `a =y^(2), b=z^(2) " and " c= x^(2), " then log"_(a) x^(3) xx "log"_(b) y^(3) xx "log"_(c)z^(3) = (27)/(8)`
Statement-2: `"log"_(b) a = (1)/("log"_(a)b)`
A. Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is true, Statement-2 is NOT a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Answer 1

Correct Answer - B
We have,
`"log"_(a) x^(3) xx "log"_(b) y^(3) xx "log"_(c)z^(3)`
`= "log"_(y^(2)) x^(3) xx "log"_(z^(2)) y^(3) xx "log"_(x^(2)) z^(3)`
`=(3)/(2)"log"_(y) x xx (3)/(2)"log"_(z) y xx (3)/(2) "log"_(x) z`
`=(27)/(8)("log"_(y) x xx "log"_(z)y xx "log"_(x) z)`
`= (27)/(8) " " [because "log"_(y)x xx "log"_(z) y = "log"_(z)x]`
In the above solution, we are using `"log"_(b) a xx "log"_(c) b = "log"_(c)a`. So, statement-2 is not the correct explanation for statement-1.