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Let x_(1) and x_(2) be two solutions of the equalition log_(x)(3x^(log_(5)x)+4) = 2log_(5)x , then the product x_(1)x_(2) is equal to

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Solution :LET `x_(1)` and `x_(2)` be two …………..
we have
`3X^(log_(5)x)+4=X^(2log_(5)x)`
`implies 3t+4=t^(2), where t = X^(log_(5)x)`
`implies t = -1 or t = 4`
`implies X^(log_(5)x)= -1`(rejected) or `X^(log_(5)x)=4`
`implies log_(5) (X^(log_(5)x)) = log_(5)4implies (log_(5)X)^(2) = log_(5)4`
`implies log_(5)x= += sqrt(log_(5)4) implies x = 5+- sqrt(log_(5)4)`
`:. x_(1)x_(2)= 5sqrt(log_(5)^(4)) x 5^(-sqrt(log_(5)^(4)) = 5^(@) = 1`


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