Question

If $log3=1.0986$ then the approximate value of $log\left(9.01\right)$ is

• A. $2.1983$
• B. $2.1893$
• C. $2.1389$
• D. $2.1789$

Answer 1

The correct option is A $2.1983$

Given ${\log }_3=1.0986$

Let $x=9$

$y=\log x$

$dy/dx=1/x$

$dy=dx/x$

$dx=0.01$

$dy=0.01/9=0.0011$

$y=\log x=\log 9=\log \left(3^2\right)=2\log 3=2\times 1.0986=2.1972$

$\log 9.01=y+dy=2.1972+0.0011=2.1983$