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Quantitative Aptitude

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If x,y,z >0 a...

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If x,y,z >0 and\ln x+\ln y+\ln z=0,then show that x^{1/\ln y +1/\ln z}.y^{1/\ln x +1/\ln z}.z^{1/\ln x+1/\ln y}=e^3 where \ln x=\log_ex.

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Q. The value of

x^{ln y - ln z} \cdot y^{ln z - ln x} \cdot z^{ln x - ln y}

(x - y ln y + y ln x) d x + x (ln y - ln x) d y = 0

x > 1, y > 1, z > 1

are in GP, then

\frac{1}{1 + l n x}, \frac{1}{1 + l n y}, \frac{1}{1 + l n z}

x^{ln (\frac{y}{z})} . y^{ln (x z)^{2}} . z^{ln (\frac{x}{y})} = 4^{4 l n y}

x > 1, y > 1

z > 1

, then which one of the following is correct?

Q. The solution of the equation

x^{2} \frac{d^{2} y}{d x^{2}}

=In ~x, when x=1, y =0 and

\frac{d y}{d x} = - 1

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