JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The sum of the roots of the equation \(x+1-2 \log _{2}\left(3+2^{x}\right)+2 \log _{4}\left(10-2^{-x}\right)=0\), is :
- A \(\log _{2} 14\)
- B \(\log _{2} 11\)
- C \(\log _{2} 12\)
- D \(\log _{2} 13\)
Answer & Solution
Correct Answer
(B) \(\log _{2} 11\)
Step-by-step Solution
Detailed explanation
\(x+1-2 \log _{2}\left(3+2^{x}\right)+2 \log _{4}\left(10-2^{-x}\right)=0\) \(\log _{2}\left(2^{x+1}\right)-\log _{2}\left(3+2^{x}\right)^{2}+\log _{2}\left(10-2^{-x}\right)=0\) \(\log _{2}\left(\frac{2^{x+1} \cdot\left(10-2^{-x}\right)}{\left(3+2^{x}\right)^{2}}\right)=0\)…
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