Question

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

Answer 1

Hello Mate!

${a}^{xyz} = { ({a}^{x} })^{yz} \\ {a}^{xyz} = { ({b}^{y} )}^{z} \\ {a}^{xyz} = {c}^{z} \\ {a}^{xyz} = a \\ xyz = 1$

Hence proved

☺!✌

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