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Solution for Show that F(X) = Loga X, 0 < a < 1 is a Decreasing Function for All X > 0 ? - CBSE (Commerce) Class 12 - Mathematics

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Question

Show that f(x) = loga x, 0 < a < 1 is a decreasing function for all x > 0 ?

Solution

\[f\left( x \right) = \log_a x\]

\[ = \frac{\log x}{\log a}\]

\[f'\left( x \right) = \frac{1}{x \log a}\]

\[\text { Since0 < a < 1 and } x > 0, f'\left( x \right) = \frac{1}{x \log a} < 0 . \]

\[\text { So,}f\left( x \right) \text { is decreasing for all } x > 0 .\]

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Solution for question: Show that F(X) = Loga X, 0 < a < 1 is a Decreasing Function for All X > 0 ? concept: Increasing and Decreasing Functions. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
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