Given that 27^1/3= 9^14 + 3^x+1
find the exact value of x

Answers

Answer 1

If the given equation is

[tex]27^{\frac13} = 9^{14} + 3^{x + 1}[/tex]

first simplify the left side using the fact that 27 = 3³:

[tex]27^{\frac13} = (3^3)^{\frac13} = 3^{\frac33} = 3^1 = 3[/tex]

and on the right side, 9 = 3²:

[tex]9^{14} = (3^2)^{14} = 3^{2\times14} = 3^{28}[/tex]

So we have

[tex]3 = 3^{28} + 3^{x + 1}[/tex]

Next,

[tex]3^{x+1} = 3^x \times 3^1 = 3 \times 3^x[/tex]

so that

[tex]3 = 3^{28} + 3 \cdot 3^x[/tex]

and dividing both side by 3 gives

[tex]1 = 3^{27} + 3^x[/tex]

Isolate 3ˣ :

[tex]3^x = 1 - 3^{27}[/tex]

Solve for x by taking the base-3 logarithm of both sides:

[tex]\log_3(3^x) = \log_3(1-3^{27})[/tex]

[tex]x \log_3(3) = \log_3(1-3^{27})[/tex]

[tex]\boxed{x = \log_3(1-3^{27})}[/tex]


Related Questions

Simplify.
1) 448
A) 5V3
C) 12V2
B) 8V
D) 10v2

Answers

Answer:

B

Step-by-step explanation:

The square root of 448 rounded up to 6 decimal places is 21.166010. It is the positive solution of the equation x2 = 448. We can express the square root of 448 in its lowest radical form as 8 √7.

geomtry plzzzzz help. me

Answers

Answer:

N=3.5

Step-by-step explanation:

it is 3.5 because it said line p is the perendicular bisector so the triangle has to be equal. so the line ZY=XY

14/4=3.5

Please answer!! Only if your answer is correct though.

Answers

Answer:

f(6) = -8  

g(-3) = 59

Step-by-step explanation:

Read other responses on other answered questions. Comment below if you'd like a detailed explanation.

there are 25 questions in a quiz
every correct answer scores 3 points
each incorrect answer loses 2 points
a question not answered scores o points.
it is possible to finish the quiz with a negative score
what is the minimum score you can get on the quiz ❓

Answers

Points obtained on the quiz increases when the points are earned from

correct responses.

The minimum score from the quiz is -50

Reasons:

The number of questions in the quiz = 25 questions

Number of points for correct answers = 3 points

Number of points lost for incorrect answers = 2 points

Points for question not answered = 0 points

Nature of total points = Positive and negative

Required:

The minimum score one can get on the quiz.

Solution:

The minimum score that can be obtained is when all responses result in a

loss of points, due to the questions being incorrect.

Therefore;

The minimum score = 25 × (-2) = -50

Learn more here:

https://brainly.com/question/19816972

​(b) If the population doubled in size over 30 months and the current population is 20,000​, what will the population be 4 years from​ now?

Answers

Answer:

The population will be 160,000 in 3 years.

Step-by-step explanation:

What is 64 minutes (1 hour and 4 minutes) as mixed number? I'm pretty sure its something like this:
[tex]1 \frac{?}{?} [/tex]
but I don't know for sure

Answers

Answer: 1  4/60

Step-by-step explanation

64 is greater then 60 . 60 = 1 hour so  64 minutes = 1 whole 4 over 60

Answer:

1 1/15.

Step-by-step explanation:

1 4/60

= 1 1/15.

1
21314 JEG B 10
3
Which is the best estimate of -14
of-14; (-20)
ם
10
-42
-28
OOOO
28
42

Answers

Step-by-step explanation:

OOOO

BYE

68% of what number is 17

Answers

Answer:

25

Step-by-step explanation:

We can set up an equation and solve for x (68% of x is 17)

68%*x=17       perform the inverse operation and divide both sides by 68%

dividing both sides by 68% will isolate the x variable

68%*x/68%= 17/68%      

x=17/68%

x=25

so, therefore,

68% of 25 is 17

Answer:

[tex]\displaystyle 11\frac{14}{25}[/tex]

Step-by-step explanation:

Whenever you take a percentage of something, you multiply. Turn 68% into a fraction and multiply by 17:

[tex]\displaystyle \frac{289}{25} = [\frac{17}{25}][17] \\ \\ \boxed{11\frac{14}{25}} = \frac{289}{25}[/tex]

I am joyous to assist you at any time.

Hello, is there anyone here a pharmacy technician?

Answers

No i am not i hope that you find who you are looking for.

-1/3 + (-7/4)

Ill give this cookie to who solves it

Answers

Answer:

-25/12

Step-by-step explanation:

first, you need a common denominator. in this case, it's 12.

-1/3=-4/12

-7/4=-21/12

and then you add

-4+-21=-25

so -25/12 is your answer

......................................

I need to know what is in the process box, it goes with the formula y=mx+b

Answers

Answer:

y= 8.5x - 10

Step-by-step explanation:

I think it is substracting because it's how much remains, if its wrong it could either be 10x - 8.5 or 8.5x + 10

A class of 22 students has taken an exam, and the mean of their scores is 76.5. One student takes the
exam late, and scores 92. After including the new score, what is the mean score for all 23 exams? Round
to the nearest hundredth.

Answers

The mean score for all 23 students is 77.17.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number.

The first step is to determine the total scores of the 22 students.

Total scores = mean score x number of students

22 x 76.5 = 1683

The second step is to add the score of the student that took the exam late tot he total scores.

New total score = 1683 + 92 = 1775

The third step is to determine the new mean score.

new mean score = new total score / total number of students

1775 / 23 = 77.17

To learn more about the mean of a set of numbers, please check: https://brainly.com/question/15420908?referrer=searchResults

Round off the decimal 55.345 to 2 decimal places.​

Answers

Answer:

Step-by-step explanation:

55.345 is rounded off two places therefore, the hundreths place

the number next to 4 is 5 in the thousandths place. 5 is high and therefore 4 is changed to 5 and makes it 53.35

Graph the equation y= -1/2x. Please help

Answers

Answer:

put one point b the negative -1 and another point by the 2 going long ways ------

Step-by-step explanation:

The temperature at the North Pole averages -36࿁F. This past winter, the temperature averaged -47࿁F. Write a correct statement that compares the absolute values of the two temperatures

Answers

Comparing the temperature average, it can be concluded that the current average temperature is higher than the past average by 11°F

The temperature difference between the present and past winter can be expressed thus :

Current temperature average = - 36°F Past average = - 47°F

Temperature difference :

-36 - (-47) = 11°F

Therefore, we can conclude that the current average temperature is higher than the past average by 11°F

Learn more : https://brainly.com/question/17225268

negative seven times a number is negative two hundred forty five. what is the number?



pleasee i need help

Answers

Answer:

35

Step-by-step explanation:

since i couldn't answer before

A teacher categorized students by whether they regularly completed their homework (or not) and whether they passed the course (or not). The data are in the table below.
Completed Homework Did not Complete Homework Total
Passed the Course 25 7 32
Did not Pass the Course 5 18 23
Total 30 25 55
A student from the class is randomly selected. Determine the following probabilites. Enter your results as percents rounded to two decimal places.
What is the probability a student passed the course given that they completed their homework?

%
What is the probability a student passed the course given that they didn't complete their homework?

28
Correct%
What is the probability a student completed their homework given that they passed the course?

%
What is the probability a student didn't complete their homework given that they didn't pass the course?

%

Answers

Probabilities are used to determine the chances of an event.

Let P represents the event that a student passes the course, and C represents the event that a student completes the assignment

(a) The probability a student passed the course given that they completed their homework?

From the table, we have:

[tex]\mathbf{n(P\ n\ C) = 25}[/tex]

[tex]\mathbf{n(C) = 30}[/tex]

So, the required probability is:

[tex]\mathbf{Pr = \frac{n(P\ n\ C)}{n(C)}}[/tex]

This gives

[tex]\mathbf{Pr = \frac{25}{30}}[/tex]

[tex]\mathbf{Pr = 0.8333}[/tex]

Express as percentage

[tex]\mathbf{Pr = 83.33\%}[/tex]

Hence, the probability a student passed the course given that they completed their homework is 83.33%

(b) The probability a student passed the course given that they didn't complete their homework

From the table, we have:

[tex]\mathbf{n(P\ n\ C'= 7}[/tex]

[tex]\mathbf{n(C') = 25}[/tex]

So, the required probability is:

[tex]\mathbf{Pr = \frac{n(P\ n\ C')}{n(C')}}[/tex]

This gives

[tex]\mathbf{Pr = \frac{7}{25}}[/tex]

[tex]\mathbf{Pr = 0.28}[/tex]

Express as percentage

[tex]\mathbf{Pr = 28\%}[/tex]

Hence, the probability a student passed the course given that they didn't complete their homework is 28%

(c) The probability a student completed their homework given that passed the course?

From the table, we have:

[tex]\mathbf{n(P\ n\ C) = 25}[/tex]

[tex]\mathbf{n(P) = 32}[/tex]

So, the required probability is:

[tex]\mathbf{Pr = \frac{n(P\ n\ C)}{n(P)}}[/tex]

This gives

[tex]\mathbf{Pr = \frac{25}{32}}[/tex]

[tex]\mathbf{Pr = 0.78125}[/tex]

Express as percentage

[tex]\mathbf{Pr = 78.125\%}[/tex]

Approximate

[tex]\mathbf{Pr = 78.13\%}[/tex]

Hence, the probability a student completed their homework given that they passed the course is 78.13%

(d) The probability a student didn't complete their homework given that they didn't pass the course

From the table, we have:

[tex]\mathbf{n(P'\ n\ C'= 18}[/tex]

[tex]\mathbf{n(P) = 23}[/tex]

So, the required probability is:

[tex]\mathbf{Pr = \frac{n(P'\ n\ C')}{n(P')}}[/tex]

This gives

[tex]\mathbf{Pr = \frac{18}{23}}[/tex]

[tex]\mathbf{Pr = 0.7826}[/tex]

Express as percentage

[tex]\mathbf{Pr = 78.26\%}[/tex]

Hence, the probability a student didn't complete their homework given that they didn't pass the course is 78.26%

Read more about probabilities at:

https://brainly.com/question/11234923

5
which ratio is greater than 5/8
12/24
3/4
15/24
4/12

Answers

Answer:(B)

Explanation: 3/4. Hope this helped :)

the vertex angle of an isosceles triangle is 50 more than twice the base angles. Find each base angle.

Answers

Answer:

Step-by-step explanation:

x + x + (2x + 50) = 180

4x = 130

x = 32.5°

HELP ME PLEASE!! I DONT WANT TO FAIL THIS AGAIN.

Answers

Answer:

A.

Step-by-step explanation:

You can see that the rate of change of function A is 3. because that's the slope (M) in y=mx+b

5 is slope for B because unit rate is 5 ( 1 to 3 change is +10 so unit rate is 5)

Which statement best explains the relationship between
lines AB and CD?
-They are parallel because their slopes are equal.
-They are parallel because their slopes are negative
reciprocals.
-They are not parallel because their slopes are not
equal.
-They are not parallel because their slopes are
negative reciprocals.

Answers

Answer:

they are parallel because their slopes are equal

Answer:

They are parallel because their slopes are equal.

Step-by-step explanation:

Find the slope using the points indicated on each line

The slope of AB

m = rise/run = 6/8 = 3/4

The slope of CD

m = rise/run = 3/4

They are parallel because their slopes are equal.

A large grocery store needs to decide how many bottles of 2 liter
Dr. Pepper to stock each week in the store. The store must decide how many bottles to stock each week. The weekly demand for 2 liter Dr. Pepper follows a Normal Distribution with a mean of 550 bottles and a standard deviation of 26 bottles. The store desires that the probability that they do not run out of 2 liter bottles of Dr. Pepper in a week to be .995.
How many bottles should they stock at the beginning of the week to have a .995 probability of not running out during the week. Choose what you believe is the best answer from the following:
i) 601,
ii) 610
iii) 617
iv) 483
v) 490
vi) none of the above

Answers

Answer:

I Kinda Confused Man

Step-by-step explanation:

I Dont Even Know The Right Answer

(PHOTO) please help need this done by tomorrow thank you.​​

Answers

Answer: 125

Step-by-step explanation: ∠4 and 55 are supplementary angles. This means that ∠4 and 55 add up to 180. We can use this to solve for ∠4.

180 - 55 = ∠4

125 = ∠4

So, ∠4 is equal to 125 degrees.

Would appreciate brainly <3

Marking as brainliest! Great the similarity statement!

Answers

Answer

1. ΔABC ≅ ΔEFG

2. ΔMKL ≅ ΔVKU

3. ΔMLN ≅ ΔNCD (With this one I couldn't fully read the letter in the middle. I couldn't tell if it was an N or a B so just swap it for the right letter. <3)

4. ΔFGH ≅ ΔRHQ

5. ΔUVL ≅ ΔMNL

6. ΔQRS ≅ ΔVUT

Step-by-step explanation:

hope this helps. . .<3

good luck! UwU

Compare:
5/14 11/18
.
>
<
=

Answers

Answer:

<

Step-by-step explanation:

hope this helps <33

Which of the following is the graph of f(x) = |x|?

Graph 1
Graph 2
Graph 3
Graph 4

Answers

Answer:

i think its the second graph

Step-by-step explanation:

please help.. no links​

Answers

Answer:

The first answer

Step-by-step explanation:

help me will mark as brainlist

Answers

Answer:

11/9 OR 1 and 2/9

Step-by-step explanation:

5/9 + 4/6

get like deonimators by mutiplying top and bottom by same thing --- afterall mutiplying by 2/2, 3/3, 4/4.. etc is mutiplying by 1... not changing anything!

So:

(2/2)*(5/9) + (3/3)(4/6) =  10/18 + 12/18 = 22/18

Which can be simplified :)

11/9 ORRR 1 and 2/9

Step-by-step explanation:

rules? I like get brainlist pleaseee :00 it's totally A

the area of a circle in terms of pi is 4pi m2. find the value of the diameter

Answers

Answer:

  4 m

Step-by-step explanation:

The area of a circle is given in terms of diameter by ...

  A = (π/4)d²

Then the diameter in terms of area is ...

  d = √(4A/π)

For the given area, the diameter is ...

  d = √(4·4π/π) = 4 . . . meters

The diameter of the circle is 4 meters.

Graph algebra problem! Can anybody help me out as graphs are definitely not my strong suit.​

Answers

Answer:

f(2) = 5

Step-by-step explanation:

Definitions:

Input values = x-coordinates.

The input values are also known as the domain, which is the set of all real numbers. With the domain of a function, you could substitute any real number into a given function for x and produce a valid output.

Output values = y-coordinates

The range is the set of all real numbers that depend on the input values plugged into the function. Thus, the range represents the output (y-values) that corresponds to the input values used into the function. Function Notation:In the function notation f(x), f  is the function name, and x is your input variable.  Output values are also called functional values.  You could use any letter to represent a function name, such as g(x), w(x), etc.,.Explanations:

This particular question asks for you to identify the corresponding output (y-value) of the given input value, x = 2.  If you look at the graph, the x-coordinate, x = 2, corresponds to the y-coordinate of 5.

Therefore, f(2) = 5.  

Attached is an edited screenshot of the graph that you posted, where it shows where f(2) = 5 is located on the graph.

Answer:

  f(2) = 5

Step-by-step explanation:

The 2 in f(2) means you're looking for the value of the function when x=2.

Find the vertical line that is the 2nd one to the right of the y-axis. Follow it up until you reach the function line (at the top edge of the graph). The y-value there is the value of f(2). That is 5 squares above the x-axis, so ...

  f(2) = 5

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