Expand the logarithm. Assume all expressions exist and are well-defined.
Write your answer as a sum or difference of common logarithms or multiples of common
logarithms. The inside of each logarithm must be a distinct constant or variable.
log 3y

Answers

Answer 1

Answer:

Step-by-step explanation:

log 3y = log(y)^3 (exponent)

or

= log(y)*log(y)*log(y)  (multiples)

Answer 2

The logarithmic expression y = log(3y) can be written as sum or difference of common logarithms as log(3y) = log(3) + log(y).

What is logarithm? What is a mathematical function, equation and expression?logarithmic : It is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number. Mathematically -

        [tex]$\log_{b}({b^x})=x[/tex]           {where [b] is logarithmic base}

function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.

Given is the following logarithmic expression as -

y = log(3y)

We have the following logarithmic expression -

y = log(3y)

Using the identity of logarithm -

log(AB) = log(A) + log(B)

log(3y) = log(3) + log(y)

Therefore, the logarithmic expression y = log(3y) can be written as sum or difference of common logarithms as log(3y) = log(3) + log(y).

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Related Questions

solve -2 1/3 - (-5)=
A: 2 2/3
B: 3 2/3
C: 3 1/3
D: -7 1/3

Answers

Answer:

A. [tex]2\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]-2\frac{1}{3} -(-5)[/tex]

[tex]-2\frac{1}{3} +5[/tex]

What order should these go in?

Answers

Answer:

1. given

2. vertical angles theorem(1st occurrence)

3. vertical angles theorem(2nd occurrence)

4. Converse of the alternative interior angles theorem

5. Transitive property of congruence

hope this helps

have a good day :)

Step-by-step explanation:

Answers:

GivenVertical Angles Theorem (1st Occurrence)Vertical Angles Theorem (2nd Occurrence)Converse of the Alternate Interior Angles TheoremTransitive Property of Congruence

========================================================

Explanation:

We always start with "given" when it comes to proofs in geometry, and proofs in general. Think of it like starting to build a house. Someone goes out and buys the material, which is the "given" that you start to work with. When we cross two lines to form an X shape, the angles opposite each other are known as vertical angles. They don't need to align vertically to be considered as such. Angles 2 and 3 fit the description. Vertical angles are always the same measure. I'm not sure why your teacher wanted to emphasize "1st occurrence" and "2nd occurrence". That part is irrelevant in my opinion.See item #2 above. Alternate interior angles are angles inside the parallel lines, and they are on alternating sides of the transversal cut. One pair of alternate interior angles is angle 3 and angle 6.The transitive property is the idea of chaining equations together. If we know that A = B and B = C, then we link them together to conclude that A = C. You can think of it as if you started in town A, moved to town B, then ultimately ended up in town C. So therefore you've gone from A to C.

help!! What is 78,400,000 expressed in scientific notation?
A. 78.4 x 10
B. 7.84 x 10
C. 78.4 x 10
D. 784 x 10

Answers

It's b the number multiplied by 10 must be less than 10

Need Help ASAP Hurry

Answers

Answer:

Step-by-step explanation:

1) Impossible, a six sided die can't have 8 if it's six sided

2) Unlikely, there isn't an equal amount of boys and girls, so it wouldn't be neither likely or unlikely or likely, or impossible

3) Likely, there are more birds than other animals

4) Neither likely nor unlikely, because there is an equal amount of short straws and long straws

find all the possible of x for which of the below is true:

[tex] \frac{2x}{x + 3} + \frac{3}{x - 3} = \frac{8}{x^{2} - 9 } [/tex]

Answers

Answer:

x = [tex]\frac{1}{2}[/tex] , x = 1

Step-by-step explanation:

Given

[tex]\frac{2x}{x+3}[/tex] + [tex]\frac{3}{x-3}[/tex] = [tex]\frac{8}{x^2-9}[/tex] ← denominator is a difference of squares

[tex]\frac{2x}{x+3}[/tex] + [tex]\frac{3}{x-3}[/tex] = [tex]\frac{8}{(x+3)(x-3)}[/tex]

Multiply through by (x + 3)(x - 3) to clear the fractions

2x(x - 3) + 3(x + 3) = 8 ← distribute left side and simplify

2x² - 6x + 3x + 9 = 8

2x² - 3x + 9 = 8 ( subtract 8 from both sides )

2x² - 3x + 1 = 0 ← in standard form

(2x - 1)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]

x - 1 = 0 ⇒ x = 1

Luis, Pedro y Ernesto fueron a comer pizza. Entre Luis y Ernesto comieron el doble que Pedro. Pedro comió el doble que Ernesto. Entre los 3 se comieron una pizza ¿Qué porción se comió cada uno?

Answers

Answer:

Luis comió 1/2 pizza, Pedro comió 1/3 pizza y Ernesto comió 1/6 pizza.

Step-by-step explanation:

Dado que Luis, Pedro y Ernesto fueron a comer pizza, y entre Luis y Ernesto comieron el doble que Pedro, y Pedro comió el doble que Ernesto, y entre los 3 se comieron una pizza, para determinar qué porción se comió cada uno se debe realizar el siguiente cálculo:  

L + P + E = 1

L + E = 2P

P = 2E

L + E = 4E

L = 4E - E

L = 3E

3E + 2E + E = 1

6E = 1

E = 1/6

E = 0.166

P = 0.166 x 2

P = 0.333

L = 0.166 x 3  

L = 0.5  

L = 1/2

Por lo tanto, Luis comió 1/2 pizza, Pedro comió 1/3 pizza y Ernesto comió 1/6 pizza.

*Question Is Above*

Answers

diameter=16 so divide by 2 to find radius
16/2=8=r

area of circle= pi*r^2

area of circle= pi*8^2

area of circle=64pi

now either leave it as an exact answer (64pi u^2) or convert it to a decimal and then round

201.06192983

round to nearest tenth= 201.1 u^2
or round to the nearest hundreth=201.06 u^2

HELPP PLZZ
ASAP TYYY

Answers

Yes, this parabola is a function because it passes the vertical line test!

The vertical line test is a test where you move left to right over a graph, and look to see if there are any instances where the vertical line touches two points at the same time. If not, then the graph is a function!

Hope this helps!! :)

Help with this’d the question?
Here’s the options ..

A (1,2)

B (3,1)

C (3,2)

D (-3,-2)

E (3,-2)

Answers

Answer: C

Step-by-step explanation:

The two lines meet at (3,2). always read these things by doing the horazontal line and then the vertical one.

Niveen makes muffins and sells them for $0.65 each. To make 12 muffins, she must spend $5.25 on muffin mix, $0.75 on vegetable oil, and $0.87 on eggs. The smallest batch of muffins Niveen can make is 12 muffins.

what would result in Niveen earning a profit?

Answers

Answer:

selling 36 muffins at a discount rate of 10% off the original price

Step-by-step explanation:

Solve for x if:

y = 7
x = 5y + 2

Solve for y if:
k = 2
8k - 3y 10

Solve for y if:
m = 3
y = 5x - 15

Solve for x and y if:
y = -3x + 9
y = 8x - 2




Answers

Answer:

Step-by-step explanation:

Please the number given in place of its letter in your equation

x = 5y + 2 if y = 7

x = 5*7 + 2

x = 35 + 2

x = 37

Apply the same principle to the others

A cable repair person has 7.9 meters of wire. Suppose each meter of the wire weighs 3.2 ounces. Find the weight of the wire.

Answers

3.2 x 7.9 = 25.28
Hope this helps:D

hey! i’ll give brainliest please help

Answers

Answer:

D

Step-by-step explanation:

hey

Answer:

I thing answer is no. D .....

What is the value of x? Show your work.
Please help

Answers

Answer:

b=5√3

Step-by-step explanation:

Find the last side of the triangle using the Pythagorean theorem.

[tex]a^{2} +b^{2} =c^{2} \\5^{2} +b^{2} =10^{2} \\b^{2} =10^{2}-5^{2}\\\\b=5\sqrt{3}[/tex]

Please help me with this one??

Answers

Answer:

Y =-25x +225

Step-by-step explanation:

First you can count the gradient first. Use then you can count y intercept

The temperature at 12:00 pm was 5oF. The temperature then went down by 1.2oF every hour till 7:00 p.m. What was the temperature at 7 pm?
If you answer and show work I’ll make you brainliest pls help

Answers

Answer:

41.6 degrees (i think, sorry if it's not.)

Step-by-step explanation:

if the amount of time from 12:00 pm to 7:00 pm was 7 hours, you're going to need to take into account that you need to lower 50 degrees 7 times by 1.2 degrees. (50 - 1.2 times 7)

Multiply 81.5 and 3.5

Answers

Answer:

285.25

Step-by-step explanation:

Basically we multiply them as normal numbers so,

815*35 = 28525

Then we take the amount of spots each number had to the RIGHT of the decimal point

81.5 = 1

3.5 = 1

1+1= 2

So: 28525. move to the left 2 times to get 285.25

Find the slant height l of the cone given the surface area S.

S=126π cm²



The slant height is
centimeters.

Answers

9514 1404 393

Answer:

  15 cm

Step-by-step explanation:

The formula for the surface area of the cone is ...

  A = πr² +πrL =  πr(r +L)

The radius of this cone is half its diameter so is (12 cm)/2 = 6 cm. Then the slant height L can be found from ...

  126π cm² = π(6 cm)(6 cm +L)

  21 cm = 6 cm +L . . . . . . . . . . . . . . divide by 6π cm

  15 cm = L . . . . . . . . . . . . . . . . subtract 6 cm

The slant height is 15 centimeters.

Ryan works part-time at a local department store.He earns 12.50 an hour . During a one week period he worked a total of 32 hours. What was Ryan's gross income for one week

Answers

Answer:

400

Step-by-step explanation:

12.50times 32

The point W is plotted on the coordinate grid below. Plot the point W’ , the reflection of W over the y-axis.

( ignore where I put a dot I just needed it to see the bottom )
PLEASE HELP ASAP

Answers

Answer:

W: (-3,5)

W': (-3,-5)

Y coordinate

Step-by-step explanation:

if you want me to explain it I can in the comments thing

In the plot the coordinates of W is (-3 , 5 ) , and the reflection will be W' (-3 , -5)

What do you mean by reflection in a graph ?

A reflection is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane.

When reflecting a figure in a line or in a point, the image is congruent to the preimage.

A reflection maps every point of a figure to an image across a fixed line.

So in the plot the coordinates of W is (-3 , 5 )

and the reflection will be W' (-3 , -5)

The plot of W and W' is attached with the answer.

To know more about reflection

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Find the inverse of function f. A.f-1(x)=7x+9 B.f-1(x)=1/9x-7/9 C.f-1(x)=7/9x-1/9 D.f-1(x)=-9x-7

Answers

Answer:

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Step-by-step explanation:

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20 POINTS!!!!!
which phrase best describes the expression : 3x + 4y + 1/2z
a. product of three variables
b. value of three coefficients
c. the quotient of three terms
d. the sum of three terms

Answers

Maybe c not to sure hope this helps

Ali earns $80 in 10 hours. How long would it take him to earn $200?

Answers

Answer:

25 hours

Step-by-step explanation:

first you ask yourself that :

if it takes just 10 hrs to make $80 , would it take more or less hours to make $200.

The answer is it will take more hours to make $200,

Based on this idea established: we say if it's giving more then less would divide.

so therefore:

we have

[tex] \frac{200}{80} \times 10 [/tex]

finally we have 25 hours.

Thanks

Identify a, b and c in the quadratic equation.

-x2 + 31x + 7 = 0

Answers

Answer:

a is -1

b is 31

c is 7

Step-by-step explanation:

-x^2+31x+1=0

ax^2+bx+c=0

fnd the value of x................

Answers

So to solve a,
You already have the first two answers which are 65 and 90. Since a tríenle always has to equal 180 you just add 65 and 90 and the subtract that number by 180 and that’s your other missing angle.
Both triangles are identical so you just have to insert the answers from the right triangle onto the left triangle.
A is the only one that I knew how to solve, sorry

S.NO.1
देहाल
खरिद मुल्य)- रु. 60,000
नाफा (P%)=5
विक्रय मुल्य =?​

Answers

Answer:

विक्रय मुल्य=रु.63000

Step-by-step explanation:

खरिद मुल्य)- रु. 60,000 (cp)

नाफा (P%)=5 (p%)

विक्रय मुल्य =? (sp)

now,

sp=(100+p%)/100×cp

(100+5)/100×6000063000

so, sp is Rs 63000.

hope it helps.

stay safe healthy and happy.

what is the value of (-35) divided by (5/7)?

Answers

Answer:

-49

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

I need help please hurry it needs to get turned in asappppp

Answers

Answer:

Did you attach a screenshot of the question? If so, we cannot see it

Step-by-step explanation:

Answer:

11.25

Step-by-step explanation:

jill has 15 feet ribbion how many yards ribbon does she have

Answers

Answer:

Step-by-step explanation

You would take 15 ft and divide it by how many feet are in a yard which is 3.

Answer - Jill has 5 yards of ribbon

Answer:

5 yards

Step-by-step explanation:

every 3 feet are 1 yard... 15 feet divided by the 3 = 5 yards

PLEASE PLEASE HELP I REALLY NEED THIS!! THANK YOU
Simplify the scale factor and write it as a proper fraction, improper fraction, or whole number.

Answers

Answer:

12 right 6 up (12,6) and 3:1 or 3

Step-by-step explanation:

Other Questions
Read this excerpt from A Black Hole is NOT a Hole.Now try this tasty thought experiment. Say some friends far outside the black hole decide to send you a snack. If they launch a red apple your way, its invisible to you at first. But keep your eyes peeled! Eventually, the apple shifts from invisible to blue, then to green, yellow, orange, and finally red, as it passes through gravitational zones that are closer and closer to the same strength as yours.Which type of graphical representation would best support a readers understanding of this excerpt?someone watching an apple hurl through spacea picnic basket being launched into spacean apple made up of all the colors mentioneda series of apples in each color mentioned Reflecting the gender stereotypes of his age group, 4-year-old Youssef is likely to say that:__________A) it is OK for boys to dress up in skirts or jewelry. B) girls cannot be doctors or police officers.C) girls can grow up to be anything they want to be.D) it is OK if boys want to play with dolls. You have just learned that the planet core of Mars is no longer radiating heat like the core of Earth. With this information what would you communicate to building designers as the lead geologist in regards to suitable building locations on the surface of Mars? Remember your informing builders about locations that would best avoid natural disasters like marsquakes and volcanoes? What evidence or theories do you have to support your statements? Which best describes the relationship betweencharacter and conflict in the excerpt? HELP! THIS IS DUE TODAY, and i will mark brainlest! Which function is a translation of the parent absolute value function?A: f(x) = 2/1B. f(x) = |x+61C. f(x) = x1D. f(x) = -4/41 Find the solution by grouping atmosphere is a present around the surface of the earth but it is not present around the surface of the Moon why A hybrid offspring of a male lion and a tigress is a _________.Plz answer I will add you as brainlest Pls do it for me thank you so much Name the disorder and symptoms in the following scenarios and describe the treatment you might suggest and why you think it is appropriate for each of the following scenarios. You can use the template below to help you organize your ideas. Maud is wandering around aimlessly. She often talks to herself. She appears to know no one and when police take her into custody, they cannot find any family. Maud continues to talk with "people" the police can neither see nor hear. She seems suspicious and "rambles on" about different topics. Name 2 types of sensory stimuli and examples of how it is used by animals. Find the vertex of the graph of the equation $y = -2x^2 + 8x - 15.$ HELP ME PLEASE! 20 POINTS! Help!!!!!!!!!!!!!!!! What is the definition of a territory?a geographic area that is politically autonomous.a political area with geographic restrictions of another country.a geographic area under political administration of another country.an independent state that is politically autonomous. 7. Which is a part of governing? YO HELP ME OUT!!!! Question is in the screenshot below PLEASE answer correctly, I am running out of time! A 40-kg crate is being lowered with a downward acceleration is 2.0 m/s2 by means of a rope. (a) What is the magnitude of the force exerted by the rope on the crate Light travels through space at a speed of 3.0 x 108 m/s. A space probe istraveling toward Earth at 2.5 * 108 m/s when one of its spotlights is turnedon. What speed would an observer on Earth measure for the light from thespotlight?O A. 2.5 * 108 m/sO B. 3.0 x 108 m/sO c. 5.5 x 108 m/sO D. 0.5 x 108 m/s