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, t
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.
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.
1 Answers
Correct Answer - A::B::C::D
` 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.