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Quantitative Aptitude

Functions

If ln x/b-c=l...

Question

If $\frac{l n x}{b - c} = \frac{l n y}{c - a} = \frac{l n z}{a - b}$ , xyz is equal to ?

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Solution

$\frac{l n x}{b - c} = \frac{l n y}{c - a} = \frac{l n z}{a - b} = k l n x = k (b - c)$
Similarly,
$l n y = k (c - a) l n z = k (a - b) l n x + l n y + l n z = k {b - c + c - a + a - b} l n (x y z) = 0 x y z = 1$

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Similar questions

\frac{ln x}{b - c} = \frac{ln y}{c - a} = \frac{ln z}{a - b}

, then which of the following option(s) is/are true ?

\frac{ln x}{b - c} = \frac{ln y}{c - a} = \frac{ln z}{a - b}

, then which of the following option(s) is/are true ?

Q. If x > 1, y > 1, z >1 are in G.P., then

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

x > 1, y > 1, z > 1

are in G.P. Then

\frac{1}{1 + ln x}, \frac{1}{1 + ln y}, \frac{1}{1 + ln z}

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}

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