If _e 4=1.3868, then _e 4.01= - Vidyadip

MCQ

If $\log _e 4=1.3868$, then $\log _e 4.01=$

A
$1.3968$
B
$1.3898$
✓
$1.3893$
D
None of these

✓

Answer

Correct option: C.

$1.3893$

Consider the function $\text{y}=\text{f(x)}=\log_\text{e}\text{x}.$
Let:
$x = 4$
$\text{x}+\triangle\text{x}=4.01$
$\Rightarrow\triangle\text{x}=0.01$
For $x = 4,$
$\text{y}\log4=1.3868$
$\text{y}=\log_\text{e}\text{x}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{1}{\text{x}}$
$\Rightarrow\Big(\frac{\text{dy}}{\text{dx}}\Big)_{\text{x}=4}=\frac{1}{4}$
$\Rightarrow\triangle\text{y}=\text{dy}=\frac{\text{dy}}{\text{dx}}\text{dx}=\frac{1}{4}\times0.01=0.0025$
$\therefore\log_\text{e}4.01=\text{y}+\triangle\text{y}=1.3893$

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