Question

If $\log 4=1.3868$, then the approximate value of $\log \left(4.01\right)$

• A. $1.3968$
• B. $1.3898$
• C. $1.3893$
• D. $1.9338$

Answer 1

The correct option is C $1.3893$

Let $y=f\left(x\right)=\log x$

Let $x=4$

$X+△x=4.01$

$△x=0.01$

For $x=4$

$Y=\log 4=1.3868$

$y=\log x$

$\frac{dy}{dx}=\frac{1}{x}=\frac{1}{4}$

$△y=dy$

$=\frac{dy}{dx}.dx$

$=\frac{1}{4}\times 0.01$

$△y=0.0025$

$\log \left(4.01\right)=y+△y$$=1.3893$