Question

If a = b^x, b = c^y and c = a^z, then what is the value of xyz?

Answer 1

$a = {b}^{x} \\ b = {c}^{y} \\ c = a {}^{z } \\ a = {b }^{x } \\ now \: since \: b = {c}^{y} \\ so \: {b}^{x} = ( {c}^{y} ) {}^{x} \\ {b}^{x} = {c}^{xy}$
$so \: a \: = {b}^{x} = {c}^{xy}$
$since \: c = {a}^{z} \\ so \: {c}^{xy} = ( {a}^{z}) {}^{xy} \\ a = {b}^{x} = {c}^{xy} = {a}^{xyz} \\ a = {a}^{xyz} \\ since \: a = {a}^{1} \\ so \: {a}^{1} = {a}^{xyz} \\ we \: can \: write \: 1 = xyz$
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