Question 1

In this unit, you learned about common logarithms. Since most calculators can be used to find the values of common logarithms only, it’s desirable to be able to convert logarithms with bases other than 10 to common logarithms. This conversion can be done using the change of base formula.


Part A

Rewrite the logarithmic equation y = logbm in exponential form.

Part B

Using a log with base c , take the log of both sides of your answer from part A. Then use the power property and solve for y .

Part C

The original equation was y=logbm . Use substitution and your answer from part B to write the change of base formula.

Part D

Watch this video for two examples of how to use the change of base formula to simplify and evaluate logarithmic expressions. Then simplify (or evaluate, if possible) this expression: log3z x logz27

Part E

Use the change of base formula and a calculator to evaluate log7 300. Round your ans

Answer and Step-by-step explanation:

Part A: Exponential equation is the "opposite" of logarithmic equation, so:

[tex]y=log_{b}m[/tex]

[tex]b^{y}=m[/tex]

Part B: Using log with base c:

[tex]log_{c}b^{y}=log_{c}m[/tex]

Power property of logarithm states that if the anti-logarithm is elevated at a power, the elevated number can be pulled in front of the logarithm:

[tex]ylog_{c}b=log_{c}m[/tex]

Solving for y:

[tex]y=\frac{log_{c}m}{log_{c}b}[/tex]

Part C: To facilitate the use of calculators, which only have values for the base-10 log and natural log, we use change of base formula, i.e., transform

[tex]y=log_{b}m[/tex]

into

[tex]y=\frac{log_{c}m}{log_{c}b}[/tex]

Part D: [tex](log_{3}z)(log_{z}27)[/tex]

Change of base will be:

[tex]log_{3}z=\frac{log_{10}z}{log_{10}3}[/tex]

[tex]log_{z}27=\frac{log_{10}27}{log_{10}z}[/tex]

Solving:

[tex](log_{3}z)(log_{z}27)[/tex] = [tex](\frac{log_{10}z}{log_{10}3})(\frac{log_{10}27}{log_{10}z} )[/tex]

[tex](log_{3}z)(log_{z}27)[/tex] = [tex]\frac{log_{10}27}{log_{10}3}[/tex]

[tex](log_{3}z)(log_{z}27)[/tex] = [tex]\frac{log_{10}3^{3}}{log_{10}3}[/tex]

[tex](log_{3}z)(log_{z}27)[/tex] = [tex]\frac{3log_{10}3}{log_{10}3}[/tex]

[tex](log_{3}z)(log_{z}27)[/tex] = 3

Part E: [tex]log_{7}300[/tex]

Using change of base:

[tex]log_{7}300=\frac{log300}{log7}[/tex]

[tex]log_{7}300=\frac{2.48}{0.85}[/tex]

[tex]log_{7}300[/tex] ≈ 3

Read the blog entry below and answer the question that follows:

At first I dreaded going to sixth grade camp. I was sure the food would be poisonous, I would freeze to death in my sleeping bag, and the other kids in my cabin would never talk to me. But was I wrong! In fact, it was the best week ever! I went horseback riding and participated in a ropes activity with a zip line course. After the course, I climbed to the top of a pole using only ropes and carabiner clips, and then I rappelled off the top. I even made a new best friend. Oh, by the way, the food was delicious. It tasted better than my mom's! (But don't tell her.)

Review the first sentence:

At first I dreaded going to sixth grade camp.

What is the connotation showing here?

A The author was impatient and could not wait to get to camp.
B The author was worried he/she might not enjoy camp.
C The author welcomed the opportunity to go to camp.
D The author was excited about going to camp.

Complete the point-slope equation of the line through (2,3)(7,4)
y-4=

HEY I NEED HELP ASAP!!!!!!!!!!!!!
this is the problem I need help with
n - 25/4 =3

What is the equation of the polynomial graphed below? NEED HELP ASAP! Will give Brainliest!

Help Please ????!!!?

What is the following equal to 7 times 10^3

John earns $6 per hour washing dishes. How many hours must he work to make at least $150?

Solve 27* 9

I will give 100 points!!!!!!

estimate 3,156-2,163 by first rounding each number to the nearest hundred ​

can someone solve this please 5(5t + 1) = 25t – 7

Identify the coefficients: -3h - 2h + 6h +9

someone please help!!!!!!!!!

f(x) = 4x + 3 and g(x) = x - 2
Solve:
g(f(x)) =

9(9r + 3s - 9)
Evaluate this

Please Help Fast! :(


Six teams are out on the field playing soccer. The teams all have the same number of players. The head coach asks for 2 players from each team to come help him move some equipment. Now there are 78 players on the field. Write and solve an algebraic equation whose solution is the number of players, p, on each team.

Please write the equation and answer please

Select the correct answer. Which function has exactly three distinct real zeros? A. h(x) = (x − 9)2(x − 4)2 B. h(x) = x(x + 7)2 C. h(x) = (x − 3)(x + 1)(x + 3)(x + 8) D. h(x) = (x − 2)2(x + 4)(x − 1)

1) 2,340/9=
What’s the answer

what are the coordinants of the turning point

A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 31% of all employees believe their company president possesses low ethical standards. Suppose 20 of a company's employees are randomly and independently sampled and asked if they believe their company president has low ethical standards and their years of experience at the company. Could the probability distribution for the number of years of experience be modelled by a binomial probability distribution?

Another way to write -7/8

A line has a slope of -3/4 and passes through the point (-5, 4) which is the equation of the line?
A: y=-3/4x + 1/4
B: y= -3/4x + 4
C: Y= -3/4x - 2
D: y= -3/4x -1/4

You are playing a video game. For each diamond you collect, you earn 110 points. You also earn 80 bonus points by completing the level in less than 2 minutes. You need to earn more than 1620 points to continue on to the next level. Write and solve an inequality that represents the numbers d of diamonds you must collect in less than 2 minutes to advance to the next level.

3.08 + 8.94 Find the sum

What is the sum of (2x2 + 5x -3) and (-3x2 -10 + x2)​

A water feature that could be a source of groundwater for humans is found at a location on a hillside where Earth’s surface is lower than the water table.


Ill mark brainliest


What type of feature might be observed at this location?


spring

aquifer

artesian well

unsaturated zone

RELATING CONCEPTS For Individual or Group Work (Exercises 105-108)

A manufacturer has fixed costs of $1000 to produce gizmos. Each gizmo costs $5 to

make. The fixed cost to produce gadgets is $750, and each gadget costs $3 to make.

Work Exercises 105-108 in order.

105. Write an expression for the cost to make x gizmos. (Hint: The cost will be the sum

of the fixed cost and the cost per item times the number of items.)

106. Write an expression for the cost to make y gadgets.

107. Write an expression for the total cost to make x gizmos and y gadgets.

108. Simplify the expression from Exercise 107.

A state forest service is conducting a study of the people who use state-operated camping facilities. The state has two camping areas, one located in the mountains and one located along the coast. The forest service wishes to estimate the average number of people per campsite during a popular weekend when all sites are expected to be used. There are 50 campsites in the mountains and 100 along the coast. From experience, the forest service knows that most sites in the mountains contain from 1-6 people and most sites along the coast contain from 1-10 people. Suppose the forest service can afford to conduct 20 interviews (e.g. they can select 20 campsites) (because they are asking many other questions in addition to number of people using the campsite and they want to do the interviews in person).
Using Neyman allocation, how would you suggest they allocate the 20 interviews among these 2 strata to minimize the standard error of the estimate of the overall average number of people per campsite?

There are 252 players on 18 teams. How many players are on each team?

Please help with question plaaseeee

Indicate the range of the function. PLEEEAAASSEEEEE!!!!