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(a^(logb x))^2-5x^(logb a)+6=0...

`(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)`

Text Solution

Verified by Experts

The correct Answer is:
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)`
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