For $y = {\log _a}x$ to be defined $'a'$ must be
For $y = {\log _a}x$ to be defined $'a'$ must be
- [IIT 1990]
- A
Any positive real number
- B
Any number
- C
$ \ge e$
- D
Any positive real number $ \ne 1$
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The value of $6+\log _{\frac{3}{2}}\left(\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \ldots}}}\right)$ is
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- [IIT 2012]
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Let $n$ be the smallest positive integer such that $1+\frac{1}{2}+\frac{1}{3}+\ldots+\frac{1}{n} \geq 4$. Which one of the following statements is true?
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- [KVPY 2017]