Let `a= log_(3) 20, b = log_(4) 15 and c = log_(5) 12`. Then find the value of `1/(a+1)+1/(b+1)+1/(c+1)`.

Explanation

To solve the problem, we need to find the value of \( \frac{1}{a+1} + \frac{1}{b+1} + \frac{1}{c+1} \) where \( a = \log_3 20 \), \( b = \log_4 15 \), and \( c = \log_5 12 \).

### Step-by-Step Solution:

1. **Rewrite \( a + 1 \), \( b + 1 \), and \( c + 1 \)**:
\[ a + 1 = \log_3 20 + 1 = \log_3 20 + \log_3 3 = \log_3 (20 \cdot 3) = \log_3 60 \]
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