CPM Homework Help : A2C Problem 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.

$\operatorname{ln} 6$
Step 1(a):
$\ln6 = \ln(2 \cdot 3)$
Step 2(a):
$\ln6 = \ln2 + \ln3$
Answer (a):
$\ln6 = (0.69315) + (1.0986)$
$\ln6 = 1.7918$

$\operatorname{ln}12$
Hint (b):
See part (a).

$\operatorname{ln} 16$
Hint (c):
See part (a).

$\operatorname { ln } \frac { 1 } { 3 }$
Step 1(d):
$\ln\frac{1}{3} = \ln\left(3^{-1}\right)$
Step 2(d):
$\ln\frac{1}{3} = -\ln3$