Question
Prove that the logarithmic function is increasing on $(0, \infty)$.
✓
Answer
Let$
f(x)=\log _e x, x>0
$
$\therefore \quad \quad f^{\prime}(x)=\frac{1}{x}=+ ve$, for $x>0$
$\Rightarrow$ for $x \leftarrow(0, \infty), f^{\prime}(x)>0$
Therefore, the given logarithmic function is increasing in $(0, \infty)$
f(x)=\log _e x, x>0
$
$\therefore \quad \quad f^{\prime}(x)=\frac{1}{x}=+ ve$, for $x>0$
$\Rightarrow$ for $x \leftarrow(0, \infty), f^{\prime}(x)>0$
Therefore, the given logarithmic function is increasing in $(0, \infty)$
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