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The equation (log(8)((8)/(x^(2))))/((log...

The equation `(log_(8)((8)/(x^(2))))/((log_(8)x)^(2))=3` has

A

no integral solution

B

one natural solution

C

two real solutions

D

one irrational solution

Text Solution

Verified by Experts

The correct Answer is:
B, C
`(log_(8)((8)/(x^(2))))/((log_(8)^(x))^(2))implieslog_(8)8-log_(6)x^(2))/((log_(8)x)^(2))=3`
put `log_(8)x=t`
Equation because `(1-2t)/(t^(2))=3`
`implies3t^(2)+2t-1=0`
`impliest=-1,(1)/(3)`
`log_(8)x=-1impliesx=(1)/(8)` ltbr and `log_(8)x=(1)/(3)impliex=2`
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