What is the sum of the roots of the equation (x+1) = 2log2(2x + 3) - 2log4(1980 - 2-x)??
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1 Answers
62\\x+1=log_2\frac{(2^x+3)^2}{(1980-2^{-x})} \\\Rightarrow 2^{x+1}=\frac{(2^x+3)^2}{(1980-2^{-x})} \\\Rightarrow (1980-2^{-x})2^{x+1}=(2^x+3)^2 \\\Rightarrow 3960.2^x-2=(2^x)^2+6.2^x+9 \\\Rightarrow (2^x)^2-3954.2^x+11=0
Which ahs two roots...
We want the sum of roots..
The product of 2 to the power of roots is 11
So sum of roots is log211
