If $a,b$ and $c$ are not equal to $0$ and $1$ and if $a^x=b,b^y=c,c^z=a$,then $xyz=?$ We have tried to solve by equation,but it can't produce the desired result.
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$\begingroup$$$a=c^z=(b^y)^z=b^{yz}=(a^x)^{yz}=a^{xyz}$$ $$xyz=1$$
$\endgroup$ 1 $\begingroup$Hint: examine $((a^x)^y)^z$ in different ways.
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