show that the sum of the roots of the equation, x+1= 2 log 2 ( 2 x +3) – 2 log 4 (1980 – 2 -x ) is log 2 11.

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Vikas TU · Answer

x+1= 2 log 2 ( 2 x +3) – 2 log 4 (1980 – 2 -x ) Can be written as: Now, x+1 = log 2 ( 2 x +3)^2 – log 2 (1980 – 2 -x ) x+1 = log 2 ( (2 x +3)^2) /(1980-2^x)) (2 x +3)^2) /(1980-2^x) = 2^(x+1) (2 x +3)^2 = (1980-2^x)*2^x.2 take 2^x = t and solve the expression.

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show that the sum of the roots of the equation, x+1= 2 log 2 ( 2 x +3) – 2 log 4 (1980 – 2 -x ) is log 2 11.

show that the sum of the roots of the equation, x+1= 2 log₂( 2^x+3) – 2 log₄(1980 – 2^-x) is log₂11.

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show that the sum of the roots of the equation, x+1= 2 log 2 ( 2 x +3) – 2 log 4 (1980 – 2 -x ) is log 2 11.

show that the sum of the roots of the equation, x+1= 2 log2( 2x+3) – 2 log4(1980 – 2-x ) is log211.

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show that the sum of the roots of the equation, x+1= 2 log₂( 2^x+3) – 2 log₄(1980 – 2^-x) is log₂11.