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Question
If `3^(x+1)=9^(x-2),` find the value of `2^(1+x)`
Solution
`3^(x+1)=9^(x-2)`
`rArr3^x xx3=9^x/9^2`
`rArr3^x xx3=(3^2)^x/(3^2)^2`
`rArr3^x xx3=3^(2x)/3^4`
`rArr3^4xx3=3^(2x)/3^4`
`rArr3^5=3^x`
Comparing both sides, we get
x = 5
So,
`2^(1+x)=2^(1+5)=2^6=64`
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