Question

The real root of $xlo{g}_{10}x=1.2$ (upto 4 decimal places) by Regula-Falsi method is

• A. 2.7210
• B. 2.7400
• C. 2.7406
• D. 2.7409

Answer 1

The correct option is C 2.7406

Let, $f\left(x\right)=xlo{g}_{10}x-1.2$
So that, $f\left(1\right)=-ve,$
$f\left(2\right)=-ve,$
and $f\left(3\right)=+ve,$
$\therefore$ the root lies between 2 and 3

Taking $x_0=2$
and $x_1=3,$
$f\left(x_0\right)=-0.59794$
and $f\left(x_1\right)=0.23236$


Using method of false position,

$x_2=x_0-\frac{x_1-x_0}{f\left(x_1\right)-f\left(x_0\right)}f\left(x_0\right)=2.7210$ ...(i)

$f\left(x_2\right)=f\left(2.7210\right)=-0.0171$
i.e. the root lies between 2.7210 and 3
$\therefore$ Taking $x_0=2.7210$
$x_1=3$
$f\left(x_0\right)=-0.0171$
and $f\left(x_1\right)=0.2313$ in equation (i), we get

$x_3=2.720+\frac{0.279}{0.2313+0.0171}\times 0.0171=2.74020$

Representing this process, successive approximations are
$x_4=2.74024$
and $x_5=2.7406$

$\therefore$ root is 2.7406, correct to 4 decimal places.