Question

if ax=b by=c cz=a then xyz is 1​

Answer 1

Step-by-step explanation:

ax=b

x=b/a

by=c

y=c/b

cz=a

z=a/c

xyz=b/a*c/b*a/c =1.

Answer 2

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Given,

${a}^{x} = b$

${b}^{y} = c$

${c}^{z} = a$

To prove:-

$xyz = 1$

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Proof:-

${a}^{x} = b$

Then,

${b}^{y} = {a}^{xy}$

Now,

${b}^{y} = c$

Then,

$c = {a}^{xy} ........(i)$

Also,

${c}^{z} = a$

Then, from equation (i)

${(a^{xy}) }^{z} = a$

Or,

${a}^{xyz} = {a}^{1}$

Comparing base, we get

$xyz = 1 \: \: \: (proved)$

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