COMEDK · Maths · 1. Basic of Mathematics
If \(\log _{2}\left(2^{x-1}+6\right)+\log _{2}\left(4^{x-1}\right)=5\), then \(x=\)
- A 4
- B 1
- C 3
- D 2
Answer & Solution
Correct Answer
(D) 2
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} &\log _{2}\left(2^{x-1}+6\right)+\log _{2}\left(4^{x-1}\right)=5 \\ &\left.\Rightarrow 2^{x-1}+6\right)\left(2^{2 x-2}\right)=2^{5} \end{aligned} \] Let \[ y=2^{x-1} \] \[ \Rightarrow \quad \cdot(y+6) y^{2}=2^{5} \]…
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