#### Question

Function f(x) = log_{a} x is increasing on R, if

(a) 0 < a < 1

(b) a > 1

(c) a < 1

(d) a > 0

#### Solution

(b) *a* > 1

\[f\left( x \right) = \log_a x = \frac{\log x}{\log a}\]

\[f'\left( x \right) = \frac{1}{x \log a}\]

\[\text { Given:f(x) is increasing on }\hspace{0.167em}R.\]

\[ \Rightarrow f'\left( x \right) > 0, \forall x \in R\]

\[ \Rightarrow \frac{1}{x \log a} > 0, \forall x \in R\]

\[ \Rightarrow a > 1\]

Is there an error in this question or solution?

Solution Function F(X) = Loga X is Increasing on R, If (A) 0 < a < 1 (B) a > 1 (C) a < 1 (D) a > 0 Concept: Increasing and Decreasing Functions.