find the value of x in the equation without evaluating the power

Find The Value Of X In The Equation Without Evaluating The Power

Answers

Answer 1

Answer:

4

Step-by-step explanation:

Here's my method of doing this:

We'll be using logarithms

Our question is:

[tex](\frac{1}{3})^{2}[/tex] × [tex](\frac{1}{3})^x[/tex] = [tex]\frac{1}{729}[/tex]

If we don't want to evaluate any powers at all we'll have to make each term have the same base (so that we can ignore the base — [tex]\frac{1}{3}[/tex])

we need to figure out what power of a [tex]\frac{1}{3}[/tex] the [tex]\frac{1}{729}[/tex] is.

what we can do is the following:

[tex](\frac{1}{3})^?[/tex] = [tex]\frac{1}{729}[/tex]

[tex]3^?[/tex] = 729

If we take the "log" of each, we can find out what power of 3 gives 729.[tex]log(3^?) = log\ 729[/tex]

We must remember this rule: [tex]log(a^n) = n \times log(a)[/tex]

[tex]? \times log 3 = log 729[/tex]

[tex]? = \frac{log\ 729}{log\ 3}[/tex]

? = 6 (with a calculator)

This means that to get 729, we need to do [tex]3^6[/tex]

Therefore [tex](\frac{1}{3})^6 = \frac{1}{729}[/tex]

We can now solve the equation!

[tex](\frac{1}{3})^{2}[/tex] × [tex](\frac{1}{3})^x[/tex] = [tex]\frac{1}{729}[/tex]

[tex](\frac{1}{3})^{2}[/tex] × [tex](\frac{1}{3})^x[/tex] = [tex](\frac{1}{3})^6[/tex]

Since each term of our equation has the same base of  [tex]\frac{1}{3}[/tex] we can ignore it and just deal with the powers!

We must remember this rule: [tex]x^a \times x^b = x^{a + b}[/tex]

Using this rule:

[tex](\frac{1}{3})^{2}[/tex] × [tex](\frac{1}{3})^x[/tex] = [tex](\frac{1}{3})^6[/tex] becomes...

[tex]2 + x = 6[/tex]

[tex]x = 6 - 2 = 4[/tex]


Related Questions

How many times would you expect your heart to beat in 25 seconds? ____________
60 seconds? _____________ 120 seconds? ___________

Answers

I thing it’s right 120 seconds

help .-. over 4 months old...

Answers

(from left to right)

____________________________________________

1 1/3 * 1 2/3

Convert to improper fractions. 4/3 * 5/3Multiply. 20/9

20/9 is your answer.

____________________________________________

1 3/8 / 1 1/12"" 11/3 / 13/12Flip the divisor and the divide sign. 11/3 * 12/13Multiply. 132/39 = 44/13

44/13 is your answer.

____________________________________________

1 2/3 / 3 1/3"" 5/3 / 10/3"" 5/3 * 3/10"" 15/30 = 1/2

1/2 is your answer.

____________________________________________

1 1/3 * 2 1/5"" 4/3 * 11/5Multiply. 44/15

44/15 is your answer.

____________________________________________

2 1/4 / 1 1/2"" 9/4 / 3/2Flip the divisor and the divide sign. 9/4 * 2/3Multiply. 18/12 = 3/2

3/2 is your answer.

____________________________________________

2 1/7 / 2 1/2"" 15/7 / 5/2"" 15/7 * 2/5"" 30/35 = 6/7

6/7 is your answer.

____________________________________________

3 2/3 * 1 1/6"" 11/3 * 7/6Multiply. 77/18

77/18 is your answer.

____________________________________________

6 1/2 / 2 2/3"" 13/2 / 8/3Flip the divisor and the divide sign. 13/2 * 3/8Multiply. 39/16

39/16 is your answer.

____________________________________________

:P

The answer is 39/16! Hope this helps with your question

3a-2b=50, 2a+3b=100 what does a equal and what does b equal?

Answers

A = (350/13) and B = (400/-13)

Whats the area of the figure below?

Answers

Answer: 63

Step-by-step explanation:

Put them into different shapes, two triangles and one trapezoid then plug in the numbers

Put them into different shapes! Do the triangle at the bottom separately and the other shape as well. The. Add together.

I need help on how to do this

Answers

You would do 8 times five times 3 and then 5 times four and add the answers together

-brainliest- do all three in the picture and show work

Answers

Answer: 1 = 120

2 = 65

3 = I can't read the no. given, but it would be 180 - (number given)

4 = 34.5

5 = 35

Step-by-step explanation:

Answer:

1.) 56.54 mm

2.) -10.28 in.

3.) 25.7 yd

Step-by-step explanation:

formula is P=1/2(3.14)d+ d

1.) P=1/2x(3.14x22)+22

3.14x22= 69.08

69.08/2= 34.54

34.54+22= 56.54

2.) P=1/2x(3.14x-4)+-4

3.14x-4= -12.56

-12.56/2= -6.28

-6.28+-4= -10.28

3.) P=1/2x(3.14×10)+10

3.14×10= 31.4

31.4/2= 15.7

15.7+10= 25.7

Help me! Well they say the sky’s the limit & to me it’s really true but my friend you haven’t seen nothing just wait till I get through! Because I’m bad!
Anyways…..this!

Answers

Answer:

b

Step-by-step explanation:

bc i am a 14 year old white boy

Find the missing side length of the right triangle

Answers

Answer:

x=16

Step-by-step explanation:

This is an unidentified triangle or a scaleneThe equation: 14^2+x^2=q^2 This equation is for the pathagoern theorem. (If you have not learned it put a thanks and ask the question about it) This equation 14^2+x^2=q^2 = 14^2=x^2-q^ = x^2= 32 = x = 16I hope this helps!

(07.06A)

Based on the graph, what is the initial value of the linear relationship?

−2

0

2/3

3

Answers

Answer:

Hello there:) I believe the answer is 2/3 and or 3 please tell me if I'm wrong ^-^

Suppose f(x) = x^2 and g(x) = (4x)^2. Which statement best compares the graph
of g(x) with the graph of f(x)?

A. The graph of g(x) is shifted 4 units to the right.
B. The graph of g(x) is horizontally stretched by a factor of 4.
C. The graph of g(x) is vertically stretched by a factor of 4.
D. The graph of g(x) is horizontally compressed by a factor of 4.

Answers

the answer would be D i hope that helps !!!!!

In jeremiah class 2/5 of the students are boys. What percent of the in jeremiah's class are boys

Answers

40% are boys. divide 2 by 5 and then multiply by 100
to get the answer, take the fraction and multiply it by 100% to get the percentage!Feel free to clarify if you’re in doubt!

what is the GCF of 10 and 8
then take the awnser for the GCF of 10 and 8 to solve this equation
10-8= __ x(__ - __)

Answers

2 is the answer for this math question

Answer:

The answer of The GCF 10 and 8 is 80

Step-by-step explanation:

What is the area of the figure?



168 centimeters squared



190 centimeters squared



238 centimeters squared



250 centimeters squared

Answers

Answer:

238 cm squared.

Step-by-step explanation:

First do (5 x 14). Divide that by 2.

Then multiply 14 x 12.

Repeat step 1 for the opposite side, (5x14)/2.

Add your totals, 35+168+35=238.

Your answer is 238 cm squared.

I got 238 just multiply 12 and 14 then add 70 because (14 x 5 divided by 2 ) x 2

HELP PLEASEEEE

a) The stop sign is a regular octagon, so the measure of ∠F must be 67.5°. What is the angle measure for ∠L? Describe the relationship between ∠F and ∠L. (1 point)
b) What is the measure of ∠E? Explain how you know. (1 point)
c) Describe the relationship between ∠E and ∠K. What is the measure of ∠K? (1 point)
d) What is the measure of ∠H? Explain. (1 point)
e) What is the measure of ∠I? Explain. (1 point)
f) Describe the relationship between ∠H and ∠L. (1 point)

Answers

Step-by-step explanation:

A) Angle L is 67.5 degrees. Angles F and L are opposite each other, yet the same angle-degree

B) e = 75°, how do i know? The triangle in the middle is isosceles so the angles on the base are equal and together with angle f, add up to 180°

C) ∠K is an alternate exterior angle.

D) ∠H is a vertical angle.

Hope this helps

What is the name of the relationship between ∠3 ​ and ∠7?
A)alternate exterior angles

B)corresponding angles

C)alternate interior angles

D)adjacent angles

Answers

Answer:

B)Corresponding angles

What is the value of x?

Answers

Answer: 56

180-33-91=56

Every triangle has a total of 180 degrees

Answer:

56

Step-by-step explanation:

The angles of a triangle add up to 180 degrees. In this case, we have 2 values.

First, we add the two values that we already have so 91 + 33 = 124

To find the length of the missing angle, we subtract 124 from 180.

180 - 124 = 56

And 56 is the value of x.

Does Anyone out there Understand this problem?
I’m really confused about what the answer should be

The equation below shows the amount of a candle that is left in ounces after burning for x hours. What is the y-intercept for this function, and what does it represent?

y
=
12

0.2
x
y=12−0.2x

A) 12; the ounces burned each hour

B) 12; the ounces in the candle before it starts burning

C) -0.2; the ounces burned each hour

D) -0.2; the ounces in the candle before it starts burning

Answers

Here it is if it is wrong just let me know

the temperature is 92 degrees. The temperature decreases for 5 hours. Each hour, the temperature decreases by 2 degrees. What is the temperature after 5 hours?


Help please!!!!

Answers

Answer:

82

Step-by-step explanation:

multiply 5 x 2 and you get ten, that is the total decrease over five hours. Subtract ten from 92 and you get 82.

The answer would be 82 degrees.

Because:
You start at 92°
Every hour you lose 2 degrees for 5 hours
5x2=10
92°-10°= 82 degrees

combine like terms 9y−4

Answers

Answer: i dont this you can combine like terms for this question because none of these have the same variable or anything.

there are no like terms, that’s the simplified form.

Find the length of the segment AB.

Answers

Answer:

8.6

Step-by-step explanation:

You need to use the Patagorean theorem! :) Just do seven squared and five squared add them up and then square root them!!

Answer: √74 or 8.6

Step-by-step explanation:

Formula for distance is  √ [ (x2 – x1)^2 + (y2 – y1)^2].A(3,9) and B(8,2)√[(8-3)^2+(2-9)^2]Put that into a calculator and you get √74 which can be rounded to 8.6

A popular art teacher at a school asks a sample of students if they would be interested in taking an art class next year. Of the 30 students he ​asks, 85​% are in one of his art classes this year. Only 15​% of the students in the school are in one of his art classes this year. Will this sample be​ biased? *


​Yes, because students who are in one of his art classes this year will be more likely to take one of his art classes next year.
​No, because students who are in one of his art classes this year will be less likely to take one of his art classes next year.
​Yes, because students who are in one of his art classes this year will be less likely to take one of his art classes next year.
​No, because students who are in one of his art classes this year will be more likely to take one of his art classes next year.

Answers

Answer:

​Yes, because students who are in one of his art classes this year will be more likely to take one of his art classes next year.

Step-by-step explanation:

Please help asap!! mark brainlyest.

Answers

Answer:

Multiply everything by 15 because when you divide 40 from 600 you get 15. We will only use the 2 numbers on the right of both samples. Then find the total of each row

18 turns into 270| 10 truns into 150 =420

19 turns into 285| 7 turns into 105=390

Headline A: Both samples show that over 300 students want to go after 8 am which makes the headline true.

Headline B: 8:30 is actually the most popular start time because both samples show greater amount of students choose 8:30 as the start time than any other time.

Headline C: This statement is not supported by the data, the data shows that 7:45 am is the second most popular selection.

Headline D: This statement is not supported by the data because both samples show that over 100 people chose 9:00.

I hope this is a good answer for you and I hope you have a nice day.

P.S. Please mark me braineast!

Headline A: Both samples show that over 300
students want to go after 8 am which makes
the headline true.
Headline B: 8:30 is actually the most popular
start time because both samples show greater
amount of students choose 8:30 as the start
time than any other time.
Headline C: This statement is not supported by
the data, the data shows that 7:45 am is the
second most popular selection.
Headline D: This statement is not supported by
the data because both samples show that over
100 people chose 9:00.

Give the other guy brainliest please

help quick pls At a company, copy machine prints 175 pages in 5 minutes. If the number of pages printed is proportional to the time, in minutes, what is the unit rate?

Answers

Answer:

the steps to get an answer is to divide 175 pages/5 making the results to be 35/1 or 35 so hopefully that is the answer and if not tell me the choices of the answer and what i did wrong.

Step-by-step explanation:

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPL PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSs

Answers

13 is the correct answer
The best answer is 13

Hellp meeeeeeeeeeeeee

Answers

Answer:

The picture is so small I cant even answer the question

Step-by-step explanation:

Making Predictions from Data (PLEASE HELP)

Answers

Answer:

here you go!

Step-by-step explanation:

1. is a group of people with one charactaristic or idea that sticks out

2. an out come of a random experiment

3. you can multiply by the amount of times

4. 3

5. 8

6. 15

7. 24

8. 468 people

9. 24 lights

10. 187 timers

( I thought I did pre good)

Two corners of the backyard are right angles. The third corner forms an obtuse angle measuring 127º. The fourth corner forms an acute angle measuring 53º. When transferring these angle measurements from the real world to the scale drawing, will their measures increase, decrease, or stay the same?

Answers

Answer: When scaling something, only the lengths of the sides change, the angles would remain the same. The answer is stay the same.

Step-by-step explanation:

URGENT! :) CAN YOU PLEASE HELP ME! 100 PTS! Ö

Answers

Answer:

the answer is 7

Step-by-step explanation:

Two steps

1. subtract the mean from each of the values and get the absolute values:

149 - 161 = -12, |-12| = 12. Do this to each value, and you will get 12, 8, 2, 5, 6 and 9.

2. Then add the values up and you will get 12 + 8 + 2 + 5 + 6 + 9 = 42

Then divide 42 by the number of values (essentially getting the mean of these numbers) so 42/6 = 7.

Thus, the final answer is 7.

There is a jar full of marbles. There are 3 red, 2 orange, 3 green and 4 blue marbles in the jar. If one marble is chosen randomly, can you list the possible outcomes ?

Answers

Answer:

{red, red, red, orange, orange, green, green, green, blue, blue, blue, and blue}

Step-by-step explanation:

I think you just list all of them, I hope it's right, if not im gonna feel stupd

for red its 1/4 chance. blue = 1/3 chance. orange = 1/6 chance. green = 1/4

The product of ages of Hasni and Alia is 32 years. Hasni is 4 years older than Alia. How old are Hasni and Alia?

Answers

The product is the answer when you multiply two numbers together. So, since Hasni is 4 years older than Alia, we need to find two numbers that are 4 apart that make 32 when we multiply them.

This gives us 8 and 4, and since Hasni js 4 years older than Alia, Hasni must be 8 years old and Alia must be 4 years old.

If the product of the ages of Hasni and Alia is 32 years and Hasni is 4 years older than Alia, then Hasni would be 8 years old while Alia would be 4 years old.

How to determine the ages

First, the question states that the product of the ages of Hasni and Alia is 32 years old. We can represent mathematically in the following way;

ab = 32

Assuming b = a + 4, then we would have;

a(a + 4) = 32 years

a² + 4a = 32 years

a+8)(a - 4) = 32 years

So, the ages are expressed as follows:

x + 8 = 0 or x - 4 = 0

Hasni's age is 8 while Alia's age is 4.

Learn more about age calculations here:

https://brainly.com/question/26423521

#SPJ2

Other Questions
Bartering was an early way that people _____ What was one of queen victorias first requests upon becoming queen?. explain the pros and cons of touchscreen, non-touchscreen, and hybrid devices: 5-16 Find the general indefinite integral.16. [tex]\int \frac{\sin 2 x}{\sin x} d x[/tex] writing an email about your holiday Why was assimilation a challenge for native americans?. Who was the first prime minister of India? Select all that apply.What is Shelley's attitude in the last stanza of "Song to the Men of England"?hopelessoptimisticsarcastichopefultrying to jar the men into action The temperature in Toronto was -5C on Wednesday. It fell by 3C on Thursday. What was Thursday's temperature? Victor Stafford Reid Literary work and education Rationalize denominator What did the United States gain from the Cuban Missile Crisis? What two organelles are includedin the endosymbiosis theory?A. mitochondria and chloroplastB. nucleus and ribosomeC. mitochondria and Golgi body Which is a property of acids in aqueous solutions?O They feel soapy.O They taste bitter.They increase the concentration of H* ions.O They decrease the concentration of H* ions. Objects in space are moving at a constant velocity in a straight line.Which phrase tells what they do?O always move in an orbitO stop on their own when they run out of energyo keep moving at a constant velocity until some force acts on themO require constant energy to keep moving in one or more directions anslate the following pairs of sentences into Spanish.Jos Antonio washes his hands.Arturo washes his car.Andrea puts on her jacket.Luisa puts the plate on the table.Tomeu sleeps in the car.Alison falls asleep at ten. Which word describes Japan and the people of Japan? Which words describe America and britain? Large cities in developing countries grow at much faster rates than in developed countries. Explain why this is so in detail. Using the drop down, complete the first column of the Punnett Square.(its the same for the t one ) Briefly explain the source, harmful effects and physical properties of oxides of nitrogen.