48. log2 (4* + 4) = log, 2* +log, (...
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48. log2 (4* + 4) = log, 2* +log, (2x+-3)

JEE/Engineering Exams
Maths
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( log _{2}left(4^{x}+4right)=log _{2} 2^{x}+log _{2}left(2^{x+1}-3right) ) ( Rightarrow log _{2}left(2^{2 x}+4right)=log _{2}left(2 cdot 2^{2 x}-3 cdot 2^{x}right) ) ( Rightarrow quad 2^{2 x}+4=2 cdot 2^{2 x}-3 cdot 2^{x} ) =) ( 2^{2 x}-3 cdot 2^{x}-4=0 quad Rightarrow quad 2^{2 x}-4 cdot 2^{x}+2^{x}-4=0 ) ( Rightarrow quadleft(2^{x}+1right)left(2^{x}-4right)=0 ) ( Rightarrow quad 2^{x}=-1 quad ) or ( quad 2^{x}=4 ) ( Rightarrow quad 2^{x} eq-1 ) ( Rightarrow quad frac{2^{x}=4}{mid x=2} )
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