If `x=log_(2a) a,y=log_(3a) 2a ` and `z=log_(4a) 3a` then prove that `xyz+1=2yz`

Explanation

To prove that \( xyz + 1 = 2yz \) given \( x = \log_{2a} a \), \( y = \log_{3a} 2a \), and \( z = \log_{4a} 3a \), we will start by calculating each logarithm and then substituting them into the left-hand side (LHS) of the equation.

### Step 1: Calculate \( x \)
We start with:
\[ x = \log_{2a} a \]
Using the change of base formula, we can rewrite this as:
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