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Solve (x^(log(10)3))^(2) - (3^(log(10)x)...

Solve `(x^(log_(10)3))^(2) - (3^(log_(10)x)) - 2 = 0`.

Text Solution

Verified by Experts

The correct Answer is:
` x = 10^(log_(3^(2)))`
Let `(x^(log_(10)3))=(3^(log_(10)x))=t`
Therefore, the given equation is
` t^(2) - t-2=0 or (t-2)(t+1) =0 `
` rArr t = 2" "("as t =- 1 is not possible")`
`rArr(3^(log_(10)x)) = 2`
` or log_(10)x = log_(3) 2`
` or x = 10^(log_(3)2)`
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