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

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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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