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 \( ab + 5(a - b) \) given \( a = \log_{12} 18 \) and \( b = \log_{24} 54 \).

### Step 1: Express \( a \) and \( b \) using change of base formula
Using the change of base formula, we can express \( a \) and \( b \) in terms of logarithms to a common base (let's use base 2):

\[ a = \frac{\log_2 18}{\log_2 12} \]
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