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Question
If `sqrt(9^x) = root(3)(9^2)`, then x = ______
Options
`2/3`
`4/3`
`1/3`
`5/3`
MCQ
Solution
`4/3`
Explanation;
Hint:
`sqrt(9^x) = root(3)(9^2)`
⇒ `(9^x)^(1/2) = (9^2)^(1/3)`
⇒ `9^(x/2) = 9^(2/3)`
`x/2 = 2/3`
3x = 4
x = `4/3`
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Fractional Index
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