WBJEE · Maths · Basic of Mathematics
The number of solutions of the equation \(\frac{1}{2} \log _{\sqrt{3}}\left(\frac{x+1}{x+5}\right)+\log _{9}(x+5)^{2}=1\) is
- A 0
- B 1
- C 2
- D infinite
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
Given equation is \(\frac{1}{2} \log _{\sqrt{3}}\left(\frac{x+1}{x+5}\right)+\log _{9}(x+5)^{2}=1\) \(\Rightarrow \quad \frac{1}{2} \cdot\left(\frac{1}{1 / 2}\right) \log _{3}\left(\frac{x+1}{x+5}\right)+\frac{1}{2} \log _{3}(x+5)^{2}=1\)…
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