Question

if a^3x=b,b^3y=c,c^3z=a find the value of x×y×z​

Answer 1

Answer:

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Answer 2

Answer:

$xyz=\frac{1}{27}$

Given:

$a^{3x}=b$

$b^{3y}=c$

$c^{3z}=a$

Step-by-step explanation:

$a^{3x}= b$

Taking log on both sides, we get,

$3x log (a) = log (b)$

$3 x=\frac{\log (b)}{\log (a)}$

$x=\frac{1}{3}$

Similarly, $b^{3y}=c$

Take log on both sides

$3y log (b) = log (c)$

$3 y=\frac{\log (b)}{\log (c)}$

$y=\frac{1}{3}$

Similarly, $c^{3z}=a$

Take log on both sides  

$3z log (c) = log (a)$

$3 z=\frac{\log (c)}{\log (a)}$

$z=\frac{1}{3}$

By multiplying the value of x and y and z we get,

$x y z=\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}=\frac{1}{27}$