If ` a ge b gt 1`, then find the largest possible value of the expression ` log_(a)(a//b)+log_(a)(b//a)`.

Explanation

To solve the expression \( \log_a\left(\frac{a}{b}\right) + \log_a\left(\frac{b}{a}\right) \), we will use the properties of logarithms step by step.

### Step 1: Rewrite the logarithmic expressions
We can use the property of logarithms that states \( \log_b\left(\frac{m}{n}\right) = \log_b(m) - \log_b(n) \). Thus, we can rewrite the given expression as:

\[ \log_a\left(\frac{a}{b}\right) = \log_a(a) - \log_a(b) \]
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