Answer
See the explanation
Work Step by Step
Law of Logarithms:
1. $\log(AB)=\log A +\log B$
2. $\log(A/B)=\log A -\log B$
3. $\log(A^C)=C\log A$
4. $\log_{A}B=\frac{\log_{C}A}{\log_{C}B}$
Properties of Loagrithms:
1. $\log_{a}1=0$
2. $\log_{a}a=1$
3. $\log_{a}a^x=x$
4. $a^{\log_{a}x}=x$
a. From the properties of logarithms (4):
$10^{\log36}=36$
b. From the properties of logarithms (3):
$\ln e^3=3$
c. From the properties of logarithms (3):
$\log_{3} \sqrt{27}=\log_{3}3^{3/2}=\frac{3}{2}$
d. From the law of logarithms (2):
$\log_{2}80-\log_{2}10=\log_{2}(80/10)=\log_{2}8=\log_{2}2^3=3$
e. From the law of logarithms (4):
$\log_{8}4=\frac{\log_{2}4}{\log_{2}8}=\frac{2}{3}$
f. From the law of logarithms (1):
$\log_{6}4+\log_{6}9=\log_{6}36=\log_{6}6^2=2$
