12. ( log 3- og 2. log(27-V3)
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12. ( log 3- og 2. log(27-V3)

JEE/Engineering Exams
Maths
Solution
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( left(1+frac{1}{2 x}right) log 3+log 2=log (27-sqrt[3]{3}) ) ( 3^{left(1+frac{1}{2 x}right) cdot 2}=3^{3}-3^{1 / x} ) ( 3^{left(1+frac{1}{2 x}right)(3-1)}=3^{3}-3^{1 / x} ) ( 3^{left(2+frac{1}{2 x}right)}-3^{left(1+frac{1}{2 x}right)}=3^{3}-3^{1 / x} ) comparing coefficients we get, begin{tabular}{c|c} ( 2+frac{1}{2 x}=3 ) & ( 1+frac{1}{2 x}=frac{1}{x} ) ( frac{1}{2 x}=1 ) & ( 1=frac{1}{2 x} ) ( sqrt{x}=1 / 2 ) & ( frac{x=1 / 2}{1} ) end{tabular} ( x=1 / 2 )
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