116965
The solution of the equation \(\log _{101} \log _7(\sqrt{x+7}+\sqrt{x})=0\) is
1 3
2 7
3 9
4 49
Explanation:
C Given, \(\log _{101} \log _7(\sqrt{\mathrm{x}+7}+\sqrt{\mathrm{x}})=0\) \(\log _7(\sqrt{\mathrm{x}+7}+\sqrt{\mathrm{x}})=1\) \(\sqrt{\mathrm{x}+7}+\sqrt{\mathrm{x}}=7\) Squaring both the sides, we get - \(x+7+x+2 \cdot \sqrt{x} \cdot \sqrt{x+7}=49\) \(2 \sqrt{x} \cdot \sqrt{x+7}=49-7-2 x\) \(=42-2 x\) \(2 \sqrt{x} \cdot \sqrt{x+7}=49-7-2 x\) Again squaring, we get - \(\mathrm{x}(\mathrm{x}+7)=(21)^2+\mathrm{x}^2-42 \mathrm{x}\) \(\text { or, } \mathrm{x}^2+7 \mathrm{x}=(21)^2+\mathrm{x}^2-42 \mathrm{x}\) \(\therefore 49 \mathrm{x}=21 \times 21\) \(\therefore \mathrm{x}=\frac{21 \times 21}{7 \times 7}=3 \times 3=9\)
WB JEE-2014
Sets, Relation and Function
116966
Consider the non-constant differentiable function \(f\) of one variable which obeys the relation \(\frac{f(x)}{f(y)}=f(x-y)\). If \(f^{\prime}(0)=p\) and \(f^{\prime}(5)=q\), then \(f^{\prime}(-5)\) is
116965
The solution of the equation \(\log _{101} \log _7(\sqrt{x+7}+\sqrt{x})=0\) is
1 3
2 7
3 9
4 49
Explanation:
C Given, \(\log _{101} \log _7(\sqrt{\mathrm{x}+7}+\sqrt{\mathrm{x}})=0\) \(\log _7(\sqrt{\mathrm{x}+7}+\sqrt{\mathrm{x}})=1\) \(\sqrt{\mathrm{x}+7}+\sqrt{\mathrm{x}}=7\) Squaring both the sides, we get - \(x+7+x+2 \cdot \sqrt{x} \cdot \sqrt{x+7}=49\) \(2 \sqrt{x} \cdot \sqrt{x+7}=49-7-2 x\) \(=42-2 x\) \(2 \sqrt{x} \cdot \sqrt{x+7}=49-7-2 x\) Again squaring, we get - \(\mathrm{x}(\mathrm{x}+7)=(21)^2+\mathrm{x}^2-42 \mathrm{x}\) \(\text { or, } \mathrm{x}^2+7 \mathrm{x}=(21)^2+\mathrm{x}^2-42 \mathrm{x}\) \(\therefore 49 \mathrm{x}=21 \times 21\) \(\therefore \mathrm{x}=\frac{21 \times 21}{7 \times 7}=3 \times 3=9\)
WB JEE-2014
Sets, Relation and Function
116966
Consider the non-constant differentiable function \(f\) of one variable which obeys the relation \(\frac{f(x)}{f(y)}=f(x-y)\). If \(f^{\prime}(0)=p\) and \(f^{\prime}(5)=q\), then \(f^{\prime}(-5)\) is
116965
The solution of the equation \(\log _{101} \log _7(\sqrt{x+7}+\sqrt{x})=0\) is
1 3
2 7
3 9
4 49
Explanation:
C Given, \(\log _{101} \log _7(\sqrt{\mathrm{x}+7}+\sqrt{\mathrm{x}})=0\) \(\log _7(\sqrt{\mathrm{x}+7}+\sqrt{\mathrm{x}})=1\) \(\sqrt{\mathrm{x}+7}+\sqrt{\mathrm{x}}=7\) Squaring both the sides, we get - \(x+7+x+2 \cdot \sqrt{x} \cdot \sqrt{x+7}=49\) \(2 \sqrt{x} \cdot \sqrt{x+7}=49-7-2 x\) \(=42-2 x\) \(2 \sqrt{x} \cdot \sqrt{x+7}=49-7-2 x\) Again squaring, we get - \(\mathrm{x}(\mathrm{x}+7)=(21)^2+\mathrm{x}^2-42 \mathrm{x}\) \(\text { or, } \mathrm{x}^2+7 \mathrm{x}=(21)^2+\mathrm{x}^2-42 \mathrm{x}\) \(\therefore 49 \mathrm{x}=21 \times 21\) \(\therefore \mathrm{x}=\frac{21 \times 21}{7 \times 7}=3 \times 3=9\)
WB JEE-2014
Sets, Relation and Function
116966
Consider the non-constant differentiable function \(f\) of one variable which obeys the relation \(\frac{f(x)}{f(y)}=f(x-y)\). If \(f^{\prime}(0)=p\) and \(f^{\prime}(5)=q\), then \(f^{\prime}(-5)\) is
116965
The solution of the equation \(\log _{101} \log _7(\sqrt{x+7}+\sqrt{x})=0\) is
1 3
2 7
3 9
4 49
Explanation:
C Given, \(\log _{101} \log _7(\sqrt{\mathrm{x}+7}+\sqrt{\mathrm{x}})=0\) \(\log _7(\sqrt{\mathrm{x}+7}+\sqrt{\mathrm{x}})=1\) \(\sqrt{\mathrm{x}+7}+\sqrt{\mathrm{x}}=7\) Squaring both the sides, we get - \(x+7+x+2 \cdot \sqrt{x} \cdot \sqrt{x+7}=49\) \(2 \sqrt{x} \cdot \sqrt{x+7}=49-7-2 x\) \(=42-2 x\) \(2 \sqrt{x} \cdot \sqrt{x+7}=49-7-2 x\) Again squaring, we get - \(\mathrm{x}(\mathrm{x}+7)=(21)^2+\mathrm{x}^2-42 \mathrm{x}\) \(\text { or, } \mathrm{x}^2+7 \mathrm{x}=(21)^2+\mathrm{x}^2-42 \mathrm{x}\) \(\therefore 49 \mathrm{x}=21 \times 21\) \(\therefore \mathrm{x}=\frac{21 \times 21}{7 \times 7}=3 \times 3=9\)
WB JEE-2014
Sets, Relation and Function
116966
Consider the non-constant differentiable function \(f\) of one variable which obeys the relation \(\frac{f(x)}{f(y)}=f(x-y)\). If \(f^{\prime}(0)=p\) and \(f^{\prime}(5)=q\), then \(f^{\prime}(-5)\) is
