Function f(x)= _ax is increasing on R, if: - Vidyadip

MCQ

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

A
$0 < a < 1$
✓
$a > 1$
C
$a < 1$
D
$a > 0$

✓

Answer

Correct option: B.

$a > 1$

$\text{f}(\text{x})=\log_\text{a}\text{x}=\frac{\log\text{x}}{\log\text{a}}$
$\text{f}\ '(\text{x})=\frac{1}{\text{x}\log\text{a}}$
Given$:\ f(x)$ is increasing on $R.$
$\Rightarrow\text{f}\ '(\text{x})>0,\forall\ \text{x}\in\text{R}$
$\Rightarrow\frac{1}{\text{x}\log\text{a}}>0,\forall\ \text{x}\in\text{R}$
$\Rightarrow\text{a}>1$

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