Question

Let $a^{x}$=b, $b^{y}$=c and $c^{z}$=a. Prove that xyz=1

Answer 1

Answer:

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Answer 2

$\huge\fbox\red{A}\huge\fbox\pink{N}\fbox\green{S}\huge\fbox\blue{W}\fbox\orange{E}\huge\fbox\red{R}$

Given:-

${a}^{x} = b \\ {b}^{y} = c \\ {c}^{z} = a$

To Prove:-

xyz = 1

Solution:-

As,

$\\ \: \bold{{a}^{x} = b}$

But Here a = $c^{z}$

$\\ \: \bold{( { {c}^{z} })^{x} = b}$

And Now c = $b^{y}$

$\\ \: \bold{( {( { {b}^{y} })^{z}) }^{x} = b}$

Now, $\;\Large{b^{yzx} = b^{1}}$

As The Bases are equal we can equate powers.

$\;\Large{\sf{\pink{xyz = 1}}}$

Hence Proved, xyz = 1