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# Solution for Prove that the Function F(X) = Loge X Is Increasing on (0, ∞) ? - CBSE (Science) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

Prove that the function f(x) = loge x is increasing on (0, ∞) ?

#### Solution

$\text { Let } x_1 , x_2 \in \left( 0, \infty \right)\text { such that } x_1 < x_2 . \text { Then },$

$x_1 < x_2$

$\Rightarrow \log_e x_1 < \log_e x_2$

$\Rightarrow f\left( x_1 \right) < f\left( x_2 \right)$

$\therefore x_1 < x_2 \Rightarrow f\left( x_1 \right) < f\left( x_2 \right), \forall x_1 , x_2 \in \left( 0, \infty \right)$

$\text { So,}f\left( x \right) \text { is increasing on }\left( 0, \infty \right).$

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Solution for question: Prove that the Function F(X) = Loge X Is Increasing on (0, ∞) ? concept: Increasing and Decreasing Functions. For the courses CBSE (Science), CBSE (Commerce), PUC Karnataka Science, CBSE (Arts)
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