1.

The roots of the equation `2^(x+2).3^((3x)/(x-1))=9` are given byA. `log_(2)((2)/(3)),-2`B. 3,-3C. `-2,1-(log3)/(log 2)`D. `1-log((2)/(3)),2`

Answer» Correct Answer - C
We have,
`2^(x+2)xx3^((3x)/(x-1))=3^(2)`
`rArr(x+2)log 2+(3x)/(x-1)log 3=2 log 3`
`rArr (x+2)log 2+((3x)/(x-1)-2)log 3=0`
`rArr (x+2)log 2+((x+2)/(x-1))log 3=0`
`rArr (x+2){log 2 +(log 3)/(x-1)}=0`
`rArr x+2=0" or ",log 2+(log 3)/(x-1)=0`
`rArrx=-" or ",x=1-(log 3)/(log 2)`


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