Question

Evaluate each logarithm. 100 Points for all questions.

Answer 1

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)=\frac14\log_55^2=\frac12\log_55=\frac12`

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

`23.\quad2\log_3√(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)=\frac16\log_33^5=\frac56\log_33=\frac56`

Answer 2

19. 1/2

21. 47

23. 3

25. 6

27. 5/6

Explanation:

all you had to do is use a calculator