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

Explanation

`a=(log_2 18)/(log_2 12)=(1+2log_2^3)/(2+log_2^3)-(1)`

`b=log_24^54`

`b=(log_2^54)/(log_2^24)=(1+3log_2^3)/(3+log_2^3)-(2)`

From equation 1

`2a+at=1+2t`

`2a-1=(2-a)t`

`t=(2a-1)/(2-a)-(a)`

`3a+bt=1+3t`

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