JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The number of solutions of the equation \(\log _{(x+1)}\left(2 x^{2}+7 x+5\right)+\log _{(2 x+5)}(x+1)^{2}-4=0, x\,>\,0\), is \(....\)
- A \(2\)
- B \(4\)
- C \(6\)
- D \(1\)
Answer & Solution
Correct Answer
(D) \(1\)
Step-by-step Solution
Detailed explanation
\(\log _{(x+1)}\left(2 x^{2}+7 x+5\right)+\log _{(2 x+5)}(x+1)^{2}-4=0\) \(\log _{(x+1)}(2 x+5)(x+1)+2 \log _{(2 x+5)}(x+1)=4\) \(\log _{(x+1)}(2 x+5)+1+2 \log _{(2 x+5)}(x+1)=4\) \(\text { Put } \log _{(x+1)}(2 x+5)=t\) \(t+\frac{2}{t}=3 \Rightarrow t^{2}-3 t+2=0\) \(t=1,2\)…
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