Question

`(a^(log_b x))^2-5x^(log_b a)+6=0`
A. `2^(log_(b)a)`
B. `3^(log_(a)b)`
C. `b^(log_(a)2)`
D. `a^(log_(b)3)`

Answer 1

Correct Answer - B::C
`(a^(log_(b)a))^(2)-5x^(log_(b)a)+6=0`
`implies(x^(log_(b)a))^(2)-5x^(log_(b)a)+6-0`
put `(x^(log_(b)a))=t`
`impliest^(2)-5t+6=0implies(t-2)(t-3)=0`
`impliest=2` to `t=3`
`implieslog_(b)x=log_(a)2`
`impliesx=b^(log_(a)2)=2^(log_(a)b)`
similarly for `t=3`
`x=b^(log_(a)3)=3^(log_(a)b)`