Solution
= Solution
Use $f(x)=x\log_2x-4$. Then $f(1)=-4$, $f(2)=-2$, and the <secant method> gives
$$
x_2=2-(-2)\frac{2-1}{-2-(-4)}=3.
$$
Writing $L=\log_2 3$, the next step is
$$
x_3=3-\frac{(3L-4)(3-2)}{(3L-4)-(-2)}=3-\frac{3L-4}{3L-2}=2.725982457878719\ldots.
$$
Thus the requested approximation is \b[$x_3=2.73$ to three <significant figures>]. All intermediate <logarithms> should be retained at higher precision before this final rounding.