if `(log)_a `x=b for permissible values of a and x then identify the statements which can be correct.
(a) If a and b are two irrational numbers then x can be rational
(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 two rational numbers then x can be rational .

Explanation

`log _{a} x=b or x=a^{b}`

(1) Fог `a=sqrt{2}^{sqrt{2}} notin Q and b=sqrt{2} notin Q, x=(sqrt{2}^{sqrt{2}})^{sqrt{2}}` which is rational.

(2) Fог `a=2 in Q a b d b=log _{2} 3 notin Q, x=3` which is гational.

(3) For` a=sqrt{2} and b=2, x=2`

(4) The option is aboviously correct.