### Home > A2C > Chapter 12 > Lesson 12.5.2 > Problem12-208

12-208.

Use the values for $\operatorname{ln} 2$ and $\operatorname{ln} 3$ given in problem 12-207 to evaluate each of the following expressions. Do not use a calculator.

1. $\operatorname{ln} 6$

$\ln6 = \ln(2 \cdot 3)$

$\ln6 = \ln2 + \ln3$

$\ln6 = (0.69315) + (1.0986)$

$\ln6 = 1.7918$

1. $\operatorname{ln}12$

See part (a).

1. $\operatorname{ln} 16$

See part (a).

1. $\operatorname { ln } \frac { 1 } { 3 }$

$\ln\frac{1}{3} = \ln\left(3^{-1}\right)$

$\ln\frac{1}{3} = -\ln3$