Solve : `log_(x^(2)16+log_(2x)64=3`.

1.	Solve : `log_(x^(2)16+log_(2x)64=3`.
Answer» Correct Answer - `x=2^(-1//3),4` `log_(x^(2))16+log_(2x)64=3` `rArr (4)/(log_(2)x^(2))+(6)/(log_(2)x)=3` Put `log_(2)x=t` `rArr (2)/(t)+(6)/(1+t)=3` `rArr 2+2t+6t=3t+3t^(2)` `rArr 3t^(2)-5t-2=0` `rArr (3t+1)(t-2)=0` `rArr t=-(1)/(3), t=2` `rArr log_(2)x=-(1)/(3)` or `log_(2)x=2` `rArr x=2^(-1//3)` or x = 4

Discussion

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