If `a^x=b ,\ b^y=c\ a n d\ c^z=a ,` prove that `x y z=1`

Explanation

To prove that \( xyz = 1 \) given the equations \( a^x = b \), \( b^y = c \), and \( c^z = a \), we can follow these steps:

### Step 1: Rewrite the equations
From the first equation \( a^x = b \), we can express \( a \) in terms of \( b \):
\[ a = b^{\frac{1}{x}} \tag{1} \]

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