JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The sum of all the real solutions of the equation \( log_{(x+3)}(6x^{2}+28x+30)=5-2log_{(6x+10)}(x^{2}+6x+9) \) is equal to:
- A 2
- B 1
- C 0
- D 4
Answer & Solution
Correct Answer
(C) 0
Step-by-step Solution
Detailed explanation
\( log_{x+3}[(x+3)(6x+10)]=5-2log_{6x+10}(x+3)^{2} \) \( 1+log_{x+3}(6x+10)=5-4~log_{6x+10}(x+3) \) Let \( log_{(x+3)}(6x+10)=A \) \( \Rightarrow A+\frac{4}{A}=4 \) or \( A=2 \) \(\Rightarrow \log _{(x+3)}(6 x +10)=2\) \(\Rightarrow 6 x+10=(x+3)^2\)…
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