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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 toA. 2B. 4C. 3D. 1 |
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Answer» Correct Answer - D 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)4 implies (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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