Function f(x)= _ax is increasing on R, if: 1. 0 < a < 1 2. a > 1 … - Vidyadip

Question

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

0 < a < 1
a > 1
a < 1
a > 0

✓

Answer

a > 1

Solution:
$\text{f}(\text{x})=\log_\text{a}\text{x}=\frac{\log\text{x}}{\log\text{a}}$
$\text{f}'(\text{x})=\frac{1}{\text{x}\log\text{a}}$
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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