Question

1. which is equivalent to 8 log(x) - 7 log(y)?

a. log(x^8/y^7)
b. log(56xy)
c. log(8x/7y)
d. log(x^7/y^8)

1. which scenario is an example of sampling?

a. tyler is conducting a survey to determine how many people in his class have an aquarium. he surveys only the students who like science.
b. david is conducting a study to determine how many vegetarians are in his high - school class. to complete the study, he surveys all of the students in the class.
c. megan is conducting an experiment to determine how many students play in the school band and also play sports. while conducting the study surveys every member of the high - school band.
d. kyle is conducting an experiment to determine how many students at his high school work a part - time job. he surveys every student at his high school by sending out surveys to the advisers.
e. nikki is conducting an experiment to determine the popular music choices for the students in her school. to complete her experiment she randomly selects students in her school from each homeroom.

1. researchers are investigating whether drinking sports drinks has an impact on lowering the risk of heart disease. they collect age, blood pressure, blood sugar, and other heart health data from people who regularly consume sports drinks and from people who do not regularly consume sports drinks.

Explanation:

Step1: Recall logarithm properties

The property of logarithms \(\log(a)-\log(b)=\log(\frac{a}{b})\) and \(\log(a^n) = n\log(a)\) are used.

Step2: Simplify \(\log(8)-\log(y)\)

Using the subtraction - property of logarithms \(\log(a)-\log(b)=\log(\frac{a}{b})\), we have \(\log(8)-\log(y)=\log(\frac{8}{y})\).

Answer:

d. \(\log(\frac{8}{y})\)