WBJEE · Maths · Basic of Mathematics
The solution of the equation \(\log _{101} \log _{7}(\sqrt{x+7}+\sqrt{x})=0\) is
- A 3
- B 7
- C 9
- D 49
Answer & Solution
Correct Answer
(C) 9
Step-by-step Solution
Detailed explanation
Given, \(\log _{101} \log _{7}(\sqrt{x+7}+\sqrt{x})=0\) \(\therefore \quad \log _{7}(\sqrt{x+7}+\sqrt{x})=(101)^{0}\) \(\Rightarrow \quad \log _{7}(\sqrt{x+7}+\sqrt{x})=1\) \(\Rightarrow \quad(\sqrt{x+7}+\sqrt{x})=7^{1}\) \(\Rightarrow \quad \sqrt{x+7}+\sqrt{x}=7\) On squaring…
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