Question

Evaluate each logarithm. 100 Points for all questions.

Answer 1

Answer:

19. 1/2

21. 47

23. 3

25. 6

27. 5/6

Step-by-step explanation:

all you had to do is use a calculator

Answer 2

Basic properties that will be used:

$\log_ab^n=n\log_ab$

$x^{1/n}=\sqrt[n]x$

$\log_aa=1$

All of these expression can be written to match on or more of the patterns above.

$19.\quad\log_5\sqrt[4]{25}=\log_5(5^2)^{1/4}=\dfrac14\log_55^2=\dfrac12\log_55=\dfrac12$

$21.\quad9\ln e^3+4\ln e^5=27\ln e+20\ln e=27+20=47$

$23.\quad2\log_3\sqrt{27}=2\log_3(3^3)^{1/2}=\log_33^3=3\log_33=3$

$25.\quad4\log_2\sqrt8=4\log_2(2^3)^{1/2}=2\log_22^3=6\log_22=6$

$27.\quad\log_3\sqrt[6]{243}=\log_3(3^5)^{1/6}=\dfrac16\log_33^5=\dfrac56\log_33=\dfrac56$