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Solution for If Loge 4 = 1.3868, Then Loge 4.01 = (A) 1.3968 (B) 1.3898 (C) 1.3893 (D) None of These - CBSE (Commerce) Class 12 - Mathematics

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Question

If loge 4 = 1.3868, then loge 4.01 =
(a) 1.3968
(b) 1.3898
(c) 1.3893
(d) none of these

Solution

(c) 1.3893

\[\text{ Consider the function } y = f\left( x \right) = \log_e x . \]

\[\text { Let }: \]

\[x = 4\]

\[x + ∆ x = 4 . 01\]

\[ \Rightarrow ∆ x = 0 . 01\]

\[\text { For }x = 4, \]

\[ y = l {og}_e 4 = 1 . 3868\]

\[y = \log_e x\]

\[ \Rightarrow \frac{dy}{dx} = \frac{1}{x}\]

\[ \Rightarrow \left( \frac{dy}{dx} \right)_{x = 4} = \frac{1}{4}\]

\[ \Rightarrow ∆ y = dy = \frac{dy}{dx}dx = \frac{1}{4} \times 0 . 01 = 0 . 0025\]

\[ \therefore \log_e 4 . 01 = y + ∆ y = 1 . 3893\]

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Solution If Loge 4 = 1.3868, Then Loge 4.01 = (A) 1.3968 (B) 1.3898 (C) 1.3893 (D) None of These Concept: Approximations.
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