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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. 
 

Grade:Select Grade

1 Answers

Vikas TU
14149 Points
5 years ago
x+1= 2 log2( 2x+3) – 2 log4(1980 – 2-x )
Can be written as:
Now,
x+1 = log2( 2x+3)^2 –  log2(1980 – 2-x )
x+1 = log2( (2x+3)^2) /(1980-2^x))
 (2x+3)^2) /(1980-2^x) =  2^(x+1)
 (2x+3)^2 = (1980-2^x)*2^x.2
take 2^x = t and solve the expression.

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