Question

${a}^{x} = b \\ {b}^{y} = c \\ {c}^{z} = a \\ prove \: xyz = 1$
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Answer 1

Here it is . Hope it will help you

Answer 2

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

$\Large{✓}$

Hope It Helps You ✌️