Answer
a. $1.7917$
b. $-0.4055$
c. $4.3944$
d. $0.5493$
Work Step by Step
$a.\ \ \ln 6=\ln (2\cdot 3)=\ln 2+\ln 3$$\approx 0.6931+1.0986=1.7917$
$b.\displaystyle \ \ \ln\frac{2}{3}=\ln 2-\ln 3\approx 0.6931-1.0986=-0.4055$
$c.\ \ \ln 81=\ln 3^{4}=4\ln 3\approx 4(1.0986)=4.3944$
$d. \displaystyle \ \ \ln\sqrt{3}=\ln 3^{1/2}=\frac{1}{2}\ln 3\approx\frac{1}{2}(1.0986)=0.5493$
