If `a=(log)_(12)18 , b=(log)_(24)54 ,` then find the value of `a b+5(a-b)dot`

Explanation

To solve the problem, we need to find the value of \( ab + 5(a - b) \) where \( a = \log_{12} 18 \) and \( b = \log_{24} 54 \).

### Step 1: Express \( a \) and \( b \) in terms of logarithms with a common base
We can use the change of base formula for logarithms:
\[ a = \log_{12} 18 = \frac{\log 18}{\log 12} \]
\[
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