Convert the following functions.
(a) Convert the exponential function, 16^8= (x^2)(y^5)(z^3)to its corresponding logarithmic function.
(b) Write the log form from Part A into the expanded log form, expression must be fully expanded

Please answer quickly! I’m giving 45 points to who ever can answer this correctly and I will crown the person the brainliest

Answers

Answer 1

Answer:

32 = 2 log₂ x + 5 log₂ y + 3 log₂ z

Step-by-step explanation:

16⁸= x²y⁵z³(2⁴)⁸ = x²y⁵z³2³² = x²y⁵z³log₂ 2³² = log₂ x²y⁵z³32 = log₂ x² + log₂ y⁵ + log₂ z³32 = 2 log₂ x + 5 log₂ y + 3 log₂ z

Related Questions

The hypotenuse of a right triangle has length 15 and one leg has length 5. The length of the other leg is

Answers

Answer:

15.81

Step-by-step explanation:

c=a^2+b^2=5^2+15^2≈ 15.81139

x root +29= root 4096​

Answers

Square root of x +29= square root of 4096

Square root of x +29=64
Square root of x=35
To find x you add an exponent on both sides
X=1225

The point Q(0, -1) is translated 6 units up. What are the coordinates of the resulting point, Q′?

Answers

Answer:

Q' (0,5)

Step-by-step explanation:

We know that original point Q is (0, -1), we are then told that it has been translated 6 units up. With being asked what is the new point coordinates, or Q'.

To solve, first we need to know what axis belongs to what.

X is left and right

Y is up and down.

Since we know that Q' is 6 units higher than Q, we need to increase the value in the y axis. (x,y)

-1 + 6

5

Therefore the coordinates to Q' is (0,5)

Answer:

(0,5)

Step-by-step explanation:

I can help

(x, y) is the order.

X is horizontal

y is vertical

If you move up 6 from -1, it goes

0  1  2  3  4  5

Therefore you will get  (0,5)

I hope I help and made it simple fro you to understand.

Can I please have brainliest?

write the multiplicative inverse of
a) -13/19​

Answers

Answer:

[tex] - \frac{19}{13} [/tex]

Step-by-step explanation:

[tex]the \: multiplicative \: inverse \: of \: \\ - \frac{13}{19} = - \frac{19}{13} [/tex]

Product of a number and its multiplicative inverse should be equal to 1.

So,

[tex] \bigg ( - \frac{13}{19} \bigg) \bigg ( - \frac{19}{13} \bigg) [/tex]

[tex]= \frac{13}{19}\times \frac{19}{13} [/tex]

[tex]=1 [/tex]

heartbreak anniversary

Answers

Answer:

Please include a picture or question of it please if you want someone to answer it.

what is the equation of the line that passes through the point (0,4) and (3,8)

Answers

Answer:

B

Step-by-step explanation:

this should be right

Answer:

[tex]y=\frac{4}{3}x + 4[/tex]

Step-by-step explanation:

I used the slope formula and slope-intercept form  y  =  m x  +  b  to find the equation.

Hope this helps:)

If θ is a second-quadrant angle and cosθ = - 2/3, then tanθ=

a. -2 (sqrt 5)/5
b. - (sqrt 5)/2
c. - (sqrt 5)/3

Answers

Answer:

since in second quadrant cos θ is negative.

Cos θ=b/h=2/3

b=2

h=3

p=√(3²-2²)

p=√5

Now

Tan θ=p/b=√5/2

since in second quadrant tanθ is negative

so

Tanθ=-√5/2

b. - (sqrt 5)/2

In second Quadrant cos is negative

cosØ=b/h=2/3

So

b=2 and h=3

Perpendicular

p²=h²-b²p²=3²-2²p²=5p=√5

tanØ=-p/b =-√5/2

Carol has 8 3/4 yards of material. She needs to use 1/3 of the material to make a dress. How many yard of material will she need to make the dress

Answers

9514 1404 393

Answer:

  2 11/12 yards

Step-by-step explanation:

Sometimes it works best to use improper fractions when multiplying mixed numbers and/or fractions.

  1/3(8 3/4) = 1/3(35/4) = 35/12 = 2 11/12

Carol will need 2 11/12 yards of the material for the dress.

Answer:

2 11/12 yards

Step-by-step explanation:

At a high school, 14% of all students play a sport and 9% of all students play a
sport and participate in a club. What is the probability that a student participates in
a club given that they also play a sport?

Answers

Answer:

0.6429

Step-by-step explanation:

Let, s = play a sport

c = participate in a club

P(s) = 0.14

P(s n c) = 0.09

probability that a student participates in

a club given that they also play a sport = P(c | s)

P(c | s) = P(c n s) / P(s)

P(c | s) = 0.09 / 0.14

P(c | s) = 0.64285

= 0.6429

There was a total of 184 teachers and students at an archery lesson.
3/4

of the teachers is equal to of the students.
2/5

How many teachers were there at the archery lesson?​

Answers

The question isn’t complete, doesn’t make sense. Can you rewrite the questions. Cuz I ain’t getting what the 2/5 or 3/4 referring to.

1. A penny is dropped from the top of the empire state building. The function h(t) = -16t^2 +1250 describes the height of the penny, h, after t seconds. How many seconds does it take for
the penny to hit the ground?
Round your answer to the nearest tenth of a second.

Answers

Answer: [tex]8.83\ s[/tex]

Step-by-step explanation:

Given

Height of the dropped penny is given by

[tex]h(t)=-16t^2+1250[/tex]

When penny hit the ground, [tex]h(t)=0[/tex]

[tex]\therefore -16t^2+1250=0\\\Rightarrow 16t^2=1250\\\\\Rightarrow t^2=\dfrac{1250}{16}\\\\\Rightarrow t=\sqrt{\dfrac{1250}{16}}\\\\\Rightarrow t=8.83\ s[/tex]

Thus, it takes 8.83 s to hit the ground.

The circumference of a circle is 132 dm, find it's diameter?​

Answers

Answer:

42.0169cm

Step-by-step explanation:

Using the formulas

C=2πr

d=2r

Solving ford

d=C

π=132

π≈42.0169cm

HELP FAST PLEASE WILL MARK BRANLIIST help with all 3 please ​

Answers

Answer:

See below

Step-by-step explanation:

5. 3x^2 y

6. x

7. 5y^2 b^2

You can factor, getting these answers shown above

Hope this Helps!

James has 16 more game cards than Fay. If they have 48 game
cards altogether, find the number of game cards James has.

Answers

Answer:

James has 32 game cards

Step-by-step explanation:

X=Fay

x+16=James

X(Fay) + (x+16) James =48

x+x+16=48

2x=32

x=16 Fay

x+16 James

16 + 16=32 James

check answer:

16 Fay + 32 James =48

16+32=48

48=48

1.5r – 3r + 8r + 2.5r​

Answers

Answer:

9r

Step-by-step explanation:

What are the characteristics of a function and how can we identify them?

Answers

Answer:

A function is a mathematical relationship where all inputs must have exactly one output. If there is more then one output for one input, then the relationship is not a function.

x is most of the time the input and y the output for an equation:

y = 2x

of course the input and output could be any variable.

Step-by-step explanation:

Have a nice day!

Identify the input values.
Identify the output values.
If each input value leads to only one output value, the relationship is a function. An easy way to determine whether a function is a one-to-one function is to use the horizontal line test on the graph of the function. To do this, draw horizontal lines through the graph. If any horizontal line intersects the graph more than once, then the graph does not represent a one-to-one function.

Plssss helppp with part B

Answers

Answer:

12:7

Step-by-step explanation:

From the diagram shown;

QS/PS = RT/PT

QS/PS = RT/PS+ST

QS/14 = RT/14+10

QS/14 = RT/24

14RT = 24QS

RT/QS = 24/14

RT/QS = 12/7

Hence the required ratio is 12:7

for which values of x is f(x) > g(x)

Answers

Answer:

Step-by-step explanation:

C ?

Subtract the product of 5 and 8 from 50.
HOW DO I WRITE THIS IN A NUMERICAL EXPRESSION?

Answers

Answer:

50-(5×8)

Step-by-step explanation:

brainliest please

a die is rolled 200 times with the following results outcome 123456 frenquency 32,36,44,20,30,38 what is the probability of rolling the given result ah number more than 3

Answers

Answer:

44%

Step-by-step explanation:

P(>3) =

P(4 or 5 or 6) =

(20 + 30 + 38)/200 =

88/200 = 0.44 or 44%


Between two friends
disbeliever, in ghost
the one a believer and other
tories

Answers

Answer:

Mean girls or Clueless

Step-by-step explanation:

Record the data in a table with the rows representing the type of music and the columns representing the weeks.

What number does element a12 represent?


90


100


150


200

Answers

Answer:

150

Step-by-step explanation:

The element a₁₂ represents the first row and second column which is 100. Then the correct option is B.

What is a histogram?

A diagram is made up of rectangles whose size is related to a variable's frequency and whose width is comparable to the training sample.

A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The a_{ij} element in a matrix, such as M, refers to the i-th row and j-th column element.

Record the data in a table with the rows representing the week and the columns representing the type of music.

The element a₁₂ represents the first row and second column which is 100. Then the correct option is B.

More about the histogram link is given below.

https://brainly.com/question/16819077

#SPJ2

Same-side interior angles always add
up to 180°. If 44 and 46 are same-side
interior angles, what is the measure of «6?
44=123°
4 6 = [?]
46

Answers

Answer:

∠6 = 57°

Step-by-step explanation:

∠6 = 180° - 123° = 57°

What's the difference in the range of temperatures recorded last year and the range of temperatures recorded two years ago?

Answers

Answer:

0°C

No Modal

Step-by-step explanation:

The range of a set is calculated by subtracting the max value by the lowest value in the set. Which using the data provided would be the following

range Last Year: 19 - 9 = 10

range 2 years ago: 17 - 7 = 10

Since we see that the range for both sets is 10 degrees then the difference is 0 degrees.

There is no modal temperature last year since no same temperature has appeared more than once.

In a study of the effect of cigarette smoking on the carbon monoxide diffusing capacity (DL) of the lung, researchers found that current smokers had DL readings significantly lower than those of either ex-smokers or nonsmokers. The carbon monoxide diffusing capacities for a random sample of n =20 current smokers are listed here:

103.768 88.602 73.003 123.086 91.052
92.295 61.675 90.677 84.023 76.014
100.615 88.017 71.210 82.115 89.222
102.754 108.579 73.154 106.755 90.479

Required:
a. Do these data that the mean DL reading for current smokers is significantly lower than 100 DL, the average for nonsmokers? Use αα=.01.
b. Find a 99% upper one-sided confidence bound for the mean DL reading for current smokers. Does this bound confirm your conclusions in part a?

Answers

Answer:

we conclude that mean DL reading for current smokers is significantly lower than 100 DL

μ ≤ 98.32

Step-by-step explanation:

Given :

H0 : μ = 100

H1 : μ < 100

Given the sample data:

103.768 88.602 73.003 123.086 91.052

92.295 61.675 90.677 84.023 76.014

100.615 88.017 71.210 82.115 89.222

102.754 108.579 73.154 106.755 90.479

Sample mean, xbar = 89.855

Sample standard deviation, s = 14.904

Test statistic :

(Xbar - μ) ÷ (s/√n)

(89.855 - 100) /(14.904/√20)

-10.145 / 3.3326357

Test statistic = - 3.044

Pvalue : using the Pvalue from T score calculator :

Pvalue = 0.00333

Pvalue < α ; Reject H0

Hence, we conclude that mean DL reading for current smokers is significantly lower than 100 DL.

b. Find a 99% upper one-sided confidence bound for the mean DL reading for current smokers. Does this bound confirm your conclusions in part a?

Tcritical at 99% (one sided) = 2.54

Upper confidence interval :

Xbar ± standard Error

Standard Error = Tcritical * s/√n

Standard Error = 2.54 * 14.904/√20 = 8.465

Upper boundary:

Xbar + standard error

89.855 + 8.465 = 98.32

μ ≤ 98.32

I need help again I don’t understand this

Answers

Answer:

i'm not too sure about the other ones but i know that 2^5 (the third choice) is an answer

Answer:

I think the answer would be the third choice

Can someone help me I know it's easy but please don't flame me in the comments.

Answers

Answer:

your answer is B

Step-by-step explanation:

i think the answer is b, x<7!

What is the area of this figure?

Answers

Answer:

[tex] 220.5 \: {yd}^{2} [/tex]

Step-by-step explanation:

Area of the figure = Area of the arc with radius 10 yd and central angle 90° + Area of rectangle with dimensions (10 + 5 - 3 = 12) 12 yd and (7 + 6 - 4 = 9) 9 yd + Area of square with dimension 4yd + Area of rectangle with dimensions 3 yd by 2 yd + Area of triangle with base 3 yd and height (5 + 3 = 8) 8 yd.

[tex] = \frac{90 \degree}{360 \degree} \times 3.14 {(10)}^{2} + 12 \times 9 + {4}^{2} \\ + 3 \times 2 + \frac{1}{2} \times 3 \times 8 \\ \\ = \frac{1}{4} \times 314 + 108 + 16 + 6 + 12 \\ \\ = 78.5 + 142 \\ \\ = 220.5 \: {yd}^{2} [/tex]

plz help I don't understand this​

Answers

Answer:

A and B tbh

Step-by-step explanation: there is only 5 prime numbers in 12 and A and B are 6 and 6 a ratio of 6:6

Thus both A and B will be right unless you can pick multiple its A and B

The answer is D! Hope it helps


What is the perimeter of the rectangle? 7cm 7cm 5cm 5cm
O 22 centimeters
O 24 centimeters
O 26 centimeters
O 28 centimeters

Answers

Answer:

24 centimeters

Step-by-step explanation:

7 + 7 + 5 + 5 = 24

have a nice day :)

Other Questions
A certain coin is a circle with diameter 18 mm. What is the exact area of either face of the coin? The exact rea of either face of the coin is mm2. (Simplify your answer. Type an exact answer in terms of re.) Place these events about Abolition in the correct order = Abolitionists grow in number = Most northern states outlaw slavery = Congress outlaws importation of African slaves to the US = The underground railroad begins find the area of the parallelogram Why did Ganesh Man Singh join the praja parishad? A patient who was in a car accident has lost their sense of smell. Which part of the brain is likely injured?medullabrain stemcerebrumcerebellumExplain if you want brainliest There are two primary means to earn income as a stockholder. The first method is dividend income and the second method is earnings from capital gains. With respect to the investor seeking dividend income, when the investor buys a stock from a corporation with a primary focus to earn dividend income they will typically expect a higher dividend on common stock versus preferred stock. Discuss the dividend payment requirements of a common stock versus preferred stock, in terms of which type of stock has a primary claim on dividend distributions. Explain why the common stock investor demands a higher dividend rate. como puedo hallar x 4) What human rights did women not have in this video? 4. Le chien son matre. (obey/prsent)5. J'ai prt mon livre . (to Jean)6. Voici la cl. Je dois rendre mes parents. (it)(Please dont use the g00gle translate HELP ME PLZZ!!!!Write an essay on Nitendo Swiches V.S. Nintendo Swich lightsInclude (Purpose, Focus and Organization, Evidence and Elaboration, Conventions, and the four elements of Modern Language Association (MLA) formatting. I need a poem for the art work named Composition With Red Blue And Yellow by Piet Mondrian I need a poem for his last name P, Q & R form a right-angled triangle. R, S & P lie on a straight line.PS = SQ and SQR = 46.Work out RPQ I give brainliest!! Identify the shape of the cross-section that is parallel to the base of the cylinder.A. CircleB. RectangleC. RhombusD. Triangle How the 3 R's help the environment Use linear regression to find an equation that would best predict a fair home price based on thecomps given below. Round each variable to 4 decimal places. I NEED HELP! PLEASECan you please help me on Part C #1-3!!!! Homemade applesauce is one of Duncan's favorite foods, so he bought 10 pounds of apples at the farmers' market. His applesauce recipe says that 8 ounces of apples make 1 cup of applesauce. How many cups of applesauce can he make with 10 pounds of apples? HELPPPPplease help me answer this question- ILL BRAINLIEST YOU PLEASE HELP ME A square has an area of 90 cm^2. Which of the following is the BEST estimate of the side length?8 feet9 feet10 feet4 feet