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Question
Function f(x) = loga x is increasing on R, if
Options
0 < a < 1
a > 1
a < 1
a > 0
Solution
a > 1
`f(x) log_a x = log_x/ log_a `
\[f'\left( x \right) = \frac{1}{x \log a}\]
\[\text { Given: f(x) is increasing on }\hspace{0.167em}R.\]
\[ \Rightarrow f'\left( x \right) > 0, \forall x \in R\]
\[ \Rightarrow \frac{1}{x \log a} > 0, \forall x \in R\]
\[ \Rightarrow a > 1\]
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