Question

State true or false:

If $a^x=b,b^y=c$ and $c^z=a$, then $xyz=1$.

• A. True
• B. False

Answer 1

The correct option is A True

$a^x=b\Rightarrow a^{xy}=b^y$ i.e. $a^{xy}=c$
Now, $a^{xyz}=c^z$ i.e. $a^{xyz}=a\Rightarrow xyz=1$
Alternative method :
$a=c^z=(b^y{)}^z=b^{yz}(a^x{)}^{yz}=a^{xyz}$
i.e. $a=a^{xyz}\Rightarrow xyz=1$