A) Convert the exponential function, 12^3=x^4 y^3 z^6, to its corresponding logarithmic function.
B) Write the log form from Part A into the expanded log form. **expression must be fully expanded for full credit**

Answers

Answer 1

The logarithmic function is ㏒ 12³ = ㏒ x⁴ · y³ · z⁶. The equation into the expanded logarithmic form is 3 · ㏒ 12 = 4 · ㏒ x + 3 · ㏒ y + 6 · ㏒ z.

How to apply logarithms on a exponential function

Logarithms are the reciprocal of exponential functions. In this question we must apply logarithms and its properties to obtain a linear-like expression in the following lines. The logarithm properties are summarized below:

㏒ₐ (b/c) = ㏒ₐ b - ㏒ₐ c     (1)

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c     (2)

㏒ₐ bⁿ = n · ㏒ₐ b     (3)

a) To obtain the corresponding logarithmic function we apply logarithms on both sides of the expression:

㏒ 12³ = ㏒ x⁴ · y³ · z⁶     (4)

The logarithmic function is ㏒ 12³ = ㏒ x⁴ · y³ · z⁶. [tex]\blacksquare[/tex]

b) The expanded logaritmic form of (4) consists in the addition and subtraction of logarithms of non-power numbers, whose formed could be found, if possible, by logarithm properties:

㏒ 12³ = ㏒ x⁴ · y³ · z⁶

㏒ 12³ = ㏒ x⁴ + ㏒ y³ + ㏒ z⁶

3 · ㏒ 12 = 4 · ㏒ x + 3 · ㏒ y + 6 · ㏒ z

The equation into the expanded logarithmic form is 3 · ㏒ 12 = 4 · ㏒ x + 3 · ㏒ y + 6 · ㏒ z. [tex]\blacksquare[/tex]

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Related Questions

$6.62 for 2 pounds of tomato’s

Answers

Answer:

$3.31 for each

Step-by-step explanation:

$6.62 divided by 2 = $3.31

Answer:

$6.62 divided by 2= $3.31

Step-by-step explanation:

What your going to do is divide 6 by 2 = 3

Next divided 62 by 2 = 32

Easy =)

Have a great day/night

Harry takes medicine every day. If the dosage is 0.2 of a gram per day, what is the total amount of medicine he consumes in a week?

Answers

Answer:

1.4 grams of medison for thr whole week combinded

Answer:

1.4 g

Step-by-step explanation:

0.2 gram per day x 7 days = 1.4 g total consumed in a week

Please I Need Help 20pts



To rent a certain meeting room, a college charges a reservation fee of $39 and an additional fee of $9.80 per hour. The math club wants to spend at most $117.40 on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room? Use t for the number of hours the meeting room is rented, and solve your inequality for t.

Answers

Answer:

0 < t ≤ 8  (in hours)

Up to (and including) 8 hours

Step-by-step explanation:

Let t = number of hours the room is rented

Given:

Reservation fee = $39Fee per hour = $9.80Maximum total cost = $117.40

Create an equation using the given information and solve for t:

⇒ 39 + 9.8t ≤ 117.4

Subtract 39 from both sides:

⇒ 9.8t ≤ 78.4

Divide both sides by 9.8

⇒ t ≤ 8

Therefore, the possible amounts of time for which they could rent the meeting room is 0 < t ≤ 8  (in hours)

Answer:

8 is the very maximum number of hours the room can be rented. As long as 8 is not exceeded, the room is rentable for what money the math club has.

Step-by-step explanation:

Givens

Maximum payment = 117.40Cost per hour = 9.80Fixed charge = 39 dollars

Formula

payment ≥ 39 + 9.80*t                where t is in hours.

Solution

117.40 ≥ 39 + 9.80*t                      Subtract 39 from both sides.

117.40 - 39 ≥9.80*t

78.40 ≥ 9.80*t                               Divide by 9.8

78.40/9.80 ≥ 9.80*t/9.80

8 ≥ t    

Answer t≥ 8

A number, n, is multiplied by −0. 7. The product is -1/2. What is the value of n?​

Answers

Step-by-step explanation:

-0.7n = -1/2

-0.7n = -0.5

n = 0.5/0.7

n = 0.715

I need to put this equation into standard form help please!
-4.9t²+7.5t+1.8=21

Answers

This equation into standard form is about 20.5
Answer:

20.5 yeah :)

"HABANG BUHAY SONG"

Umberto bought a car for 28,000 the car is depreciating ata rate of 9% per year what wil be the approximent value of the car after 5 years

Answers

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &28000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years\dotfill &5\\ \end{cases} \\\\\\ A=28000(1 - 0.09)^{5}\implies A=28000(0.91)^5\implies A\approx 17472.90[/tex]

Need help
read the question first

Answers

Answer:

  A. horizontal velocity is constant at 25 m/s in every interval

  B. downward velocity increases by 9.8 m/s each second, to 19.6 m/s, 29.4 m/s, 39.2 m/s, 49.0 m/s

Step-by-step explanation:

A.

Since the ball is not rocket-powered, it has no acceleration in the horizontal direction. (We ignore slowing due to air friction.) The horizontal velocity remains constant at 25 m/s.

__

B.

The vertical acceleration is given as 9.8 m/s² in the downward direction. That is, each second the ball is in motion, its velocity downward increases by 9.8 m/s. The table can be filled with ...

  t = 2 s, v = -19.6 m/s

  t = 3 s, v = -29.4 m/s

  t = 4 s, v = -39.2 m/s

  t = 5 s, v = -49.0 m/s

__

The sign is negative because the direction is downward. Positive is up.

How to solve (3x)^0 for applying the exponent rule for zero exponents

Answers

Any 0 power or exponent is equals to 1
So the answer is 1

What is 3^2, 5^3, and 9^2? I need some test help.

Answers

Answer:

3^2=9 5^3=125 9^2=81

Step-by-step explanation:

exponent is just multiplying the base by itself however we many times the exponent's (the small number on the top right of the base) value is

base-->5^3<--exponent

3^2=3×3=9

5^3=5×5×5=125

9^2=9×9=81

example

6^4=6×6×6×6=1296

a student claims y=1 is not a linear equation because it does have the form y=mx+b. Do you agree or disagree explain why

Answers

The student is wrong because y = 1 represent lienar equation of a horizontal line. Disagree.

What is Linear Equation in Slope-intercept Form?

Equation of a line in slope-intercept form, is y = mx + b, where m is the slope and b is the y-intercept of the linear graph.

Where m (slope) = 0, the linear equation would be, y = b, which suggest that the line is horizontal, and intersects the y-axis at point b.

Therefore, the student is wrong because y = 1 represent lienar equation of a horizontal line. Disagree.

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Madden needs to choose an object for his math project that shows volume. He has a choice between a container for catching bugs and a poster from his favorite movie. Which item should Madden choose and why?

Answers

Answer:

container for catching bugs because posters have nothing to do with volume

Answer:

I think Madden should go for the poster because poster have more angles as well as width length and height.

Step-by-step explanation:

Brainliest??????

Huuuurrrryyy Pllllzzzzz!!!!?!???!!


A garden measuring 8 feet by 12 feet will have a walkway around it. The walkway

has a uniform width, and the area covered by the garden and the walkway is

192 square feet. What is the width of the walkway?

A. 2 feet

B. 3. 5 feet

C. 4 feet

D. 6 feet

Answers

By solving a quadratic equation, we will see that the width of the walkway is 3ft.

How to get the width of the walkway?

Remember that for a rectangle of length L and width W, the area is:

A = W*L

Now, we know that for our garden we have:

W = 8ft

L = 12ft

If we add a walkway of width x around the garden, then the new measures are:

W' = 8ft + 2x

L' = 12ft + 2x

So the area is:

A' = ( 8ft + 2x)*( 12ft + 2x)

And we know that it is equal to 192 ft^2, then:

192 ft^2 = ( 8ft + 2x)*( 12ft + 2x)

Now we can solve this for x.

192ft^2 = 96ft^2 + 4x^2 + 20ft*x

0 = 96ft^2 - 192ft^2 + 20ft*x + 4x^2

0 = -96ft^2 + 20ft*x + 4x^2

This is a quadratic equation, and the solutions are given by the Bhaskara's formula:

[tex]x = \frac{-20ft \pm \sqrt{(20ft)^2 - 4*4*(-96ft^2)} }{2*4} \\\\x = \frac{-20ft \pm 44ft}{8}[/tex]

We only take the positive solution, so we get:

x = (-20ft + 44ft)/8 = 3ft

So the width of the walkway is 3ft.

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Find an equation for the line that passes through the points (6, -1) and (-6, 2).

Answers

Answer:

[tex]D : y = \frac{-1}{4}x + \frac{1}{2}[/tex]

Step-by-step explanation:

let D be the line that passes through the points (6, -1) and (-6, 2)

Then D has an equation of the form D: y = ax + b

Now we need to find a and b in order to be able to write the equation of the line D:

[tex]a = \frac{-1-2}{6-(-6)}= \frac{-3}{12}= \frac{-1}{4}[/tex]

Since the point (6 , -1) lies on the line D then :

-1 = (-1/4) × (6) + b

then

-1 = (-6/4) + b

then 

b = -1 - (-6/4) = -1 + 6/4 = -4/6 + 6/4 = (-4+6)/4 = 2/4 = 1/2

then

b = 1/2

Conclusion:

Since a = -1/4 and b = 1/2 then

[tex]D : y = \frac{-1}{4}x + \frac{1}{2}[/tex]

A car can travel 294 kilometers on 21 liters of gasoline. How much gasoline will it need to go 42 kilometers?

Answers

Answer:

7

Step-by-step explanation:

Latoya drove 585 miles in 9 hours. At the same rate, how many miles would she drive in 13 hours?

Answers

Answer:

845 miles

Step-by-step explanation:

Hope this helps!

WILL GIVE BRAINLIESTTT, FIVE STARS, AND THANKS
can someone explain this to me and what the question means and is asking?

Answers

The x-intercepts represent when the ball is at height=0

In other words, it shows when the ball hits the ground.

Determine the amplitude or period as requested.

Period of y = negative one-third sine 2 x
a.
Negative one-third
b.
StartFraction pi Over 3 EndFraction
c.
One-third
d.
Pi

Answers

C. One- third. Plato!!

The time period of the given function will be π.

What is a expression? What is a mathematical equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the following expression -

y = (-1/3)sin(2x)

We have -

y = (-1/3)sin(2x)

We can write -

ωx = 2x

Now -

ω = 2π/T

(2π/T)x = 2x

2π/T = 2

T = 2π/2

T = π

Therefore, the time period of the given function will be π.

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help me I need to make sure I got the correct answer.

Answers

Answer:

I dont know pls ask you parents...

Step-by-step explanation:

I dont know

Fill in the missing numbers

Answers

Answer:

(x - 4)

Step-by-step explanation:

x² - x - 12

to factor consider the factors of the constant term (- 12) which sum to give the coefficient of the x- term (- 1)

the factors are + 3 and - 4 , since

3 × - 4 = - 12 and + 3 - 4 = - 1 , then

x² - x - 12 = (x + 3)(x - 4) ← in factored form

Can someone help me solve this problem? 100-[5×(3+4)]​

Answers

solve the first bracket first (3+4)
so you have 100-[5x7]
then you do the next bracket [5x7]
so you have 100-35
100-35=65
:)

Answer:

65

Step-by-step explanation:

Use PEDMAS

P - Parenthesis ; E - exponents ; D -division ; M - mulitplication ;

A - Addition ;  S- subtraction.

First do the operation in the inner most parenthesis.

100 - [ 5 *(3 + 4)] = 100 - [ 5* 7 ]   {Now the outer parenthesis}

                             = 100 - 35

                             =  65

An atrium is being designed to house an exhibit of tropical birds. The atrium must enclose 250,000 cubic feet of space, and the designer wants it to have the shape of a hemisphere. Is such a design possible given that the plot of land on which it will be built is a rectangle 90 feet wide and 100 feet long?

Answers

The proposed design of the atrium (V < V') is possible since its volume is less than the maximum possible atrium.

Can this atrium be built in the rectangular plot of land?

The atrium with the maximum allowable radius (R), in feet, is represented in the image attached. The real atrium is possible if and only if the real radius (r) is less than the maximum allowable radius and therefore, the real volume (V), in cubic feet, must be less than than maximum possible volume (V'), in cubic feet.

First, we calculate the volume occupied by the maximum allowable radius:

V' = (8 · π / 3) · (45 ft)³

V' ≈ 763407.015 ft³

The proposed design of the atrium (V < V') is possible since its volume is less than the maximum possible atrium. [tex]\blacksquare[/tex]

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9(3+x)=4(3+x)
Answer with steps

Answers

Answer:

x = 2.5

Step-by-step explanation:

Expand the brackets[tex]27+9x=12+3x[/tex]Subtract 3x from both sides[tex]27+6x=12[/tex]Subtract 27 from both sides[tex]6x=-15[/tex]Divide both sides by 6[tex]x=2.5[/tex]

Answer:

x = -3

Step-by-step explanation:

9(3+x) = 4(3+x)

9(3+x) - 4(3+x) = 0

(9-4)(3+x) = 0

5(3+x) = 0

15+5x = 0

-15 = 5x

x = -3

pls help this is due in a bit

Answers

Answer:

multiply base area by 2 , and add the base perimiter and height

Step-by-step explanation:

hope this helped

Pls Pls help!! It's due soon!!

Answers

Answer:

-2,4

Step-by-step explanation:

to do a reflection across the y axis, apply -x,y to your coordinates

For the inverse variation equation xy = k, what is the constant of variation, k, when x = 7 and y = 3? three-sevenths seven-thirds 10 21

Answers

The value of the constant k when the value of x and y is 7 and 3 respectively in the equation xy=k is 21.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The value of the constant k when the value of x and y is 7 and 3 respectively in the equation xy=k can be written as,

[tex]xy=k\\\\(7) \times (3 ) =k\\\\k= 21[/tex]

Hence, the value of the constant k when the value of x and y is 7 and 3 respectively in the equation xy=k is 21.

Learn more about Equation:

https://brainly.com/question/2263981

Answer:

D

Step-by-step explanation:

K=21

please help me with this
Thanks~

Answers

the one above, (-6,8)

Answer:

(-6,8)

Step-by-step explanation:

line A is perpendicular to line B. if the slope of line A is -5/3, what is the slope of line B?

Answers

Answer: 3/5

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals of each other.

PLS HELPPP I HAVE NO IDEA WHAT THIS IS HELPPPPP

Answers

The volume of the whole object is 12.


If you split the object in two, the top rectangle and the bottom, then you can calculate both the volumes and add them together. The top part is 1*2*2=4, the bottom is 4*2*1=8, 8+4=12.

Ps. The star (*) is a multiplication symbol.

0.21 Divided by 7 I would like to know how to solve the equation

Answers

Answer:

0.03

Step-by-step explanation:

[tex] \frac{0.21}{7} [/tex]

==>

[tex] \frac{0.21 \times 100}{7 \times 100} [/tex]

===>

[tex] \frac{21}{7} \times \frac{1}{100} [/tex]

==>

[tex]3 \times \frac{1}{100} [/tex]

==>

[tex] \frac{3}{100} [/tex]

==>

[tex]0.03[/tex]

What is b if a=2x and c= 8x on a right triangle

Answers

B is 5.625

A=2x

C=8x

5.625x2(x)*8(x)=90

If I got this right pls give brainlest.

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