If `(log)_a x=b` for permissible values of `aa n dx ,` then identify the statement(s) which can be correct. If `aa n db` are two irrational numbers, then `x` can be rational. If `a` is rational and `b` is irrational, then `x` can be rational. If `a` is irrational and `b` is rational, then `x` can be rational. If `aa n d b` are rational, then `x` can be rational.

Options

A. If a and b are two irrational numbers, then x can be retional.
B. If a is rational and b is irrational, then x can be rational.
C. If a is irrational and b is rational, then x can be rational.
D. If a and b are rational, then x can be rational.

Answer

A, B, C, D

Explanation

` log_(a) x = b or x = a^(b)`
(1) For `a=sqrt2^(sqrt2)!inQ and b = sqrt2 !in Q, x = (sqrt2^(sqrt2))^(sqrt2)` which is rational.
(2) For ` a = 2 in Q abd b = log_(2) 3 !in Q , x = 3` which is rational.
(3) For ` a = sqrt2 and b = 2 , x = 2`
(4) The option is aboviously correct.