1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nana76 [90]
2 years ago
7

If 3 to the power y = x then y = ?

Mathematics
1 answer:
Oksanka [162]2 years ago
6 0

Answer:

y=\log_3(x)


Step-by-step explanation:

3^y=x

\ln(3^y)=\ln(x)

y\ln(3)=\ln(x)

y=\frac{\displaystyle\ln(x)}{\displaystyle\ln(3)}

but if

f(x)=\frac{\displaystyle\ln(x)}{\displaystyle\ln(3)}

then since

f(3)=\frac{\displaystyle\ln(3)}{\displaystyle\ln(3)}=1

f(x)=\log_3(x)

so

y=\log_3(x)


or


3^y=x

\log_3(3^y)=\log_3(x)

y\log_3(3)=\log_3(x)

\text{but }\,\log_3(3)=1, \text{so,}

y=\log_3(x)



You might be interested in
With bases V1, V2 , V3 andw1, w2 , W3, suppose T(v1) = w2 and T(v2) = T(v3) = w1 + w3 . T is a linear transformation. Find the m
Roman55 [17]

Answer:

See picture and explanation below.

Step-by-step explanation:

With this information, the matrix A that you can find is the transformation matrix of T. The matrix A is useful because T(x)=Av for all v in the domain of T.

A is defined as T=([T(v_1)] [T(v_2] [T(v_3)])\text{ where }[T(v_i)] denotes the vector of coordinates of T(v_i) respect to the basis (we can apply this definition because forms a basis for the domain of T).

The vector of coordinates can be computed in the following way: if T(v_i)=a_1w_1+a_2w_2+a_3w_3 then [T(v_i)]=(a_1,a_2,a_3)^t.

Note that we have all the required information: T(v_1)=0w_1+1\cdot w_2+0w_3 then [T(v_1)]=(0,1,0)^t

T(v_2)=T(v_3)=1\cdot w_1+0w_2+0w_3 hence [T(v_2)]=[T(v_3)]=(1,0,0)^t

The matrix A is on the picture attached, with the multiplication A(1,1,1).

Finally, to obtain the output required at the end, use the properties of a linear transformation and the outputs given:

T(v_1+v_2+v_3)=T(v_1)+T(v_2)+T(v_3)=w_2+w_1+w_1=w_2+2w_1  

In this last case, we can either use the linearity of T or multiply by A.

4 0
3 years ago
Miles sells 3 raffle tickets for $18 and 4 tickets for $24. The pattern for the price of the tickets is the same. How much money
serg [7]

Answer:

If Miles sells 6 tickets the money he will collect be <u>$36</u>.

Step-by-step explanation:

Given:

Miles sells 3 raffle tickets for $18 and 4 tickets for $24.

The pattern for the price of the tickets is the same.

Now, to find the money miles will collect if he sells 6 tickets.

Let the money Miles will collect be x.

The ticket if sells will be 6.

As, Miles sells 3 tickets for $18.

And the pattern for the price is same.

<em>So, 3 is equivalent to 18.</em>

<em>And, 6 is equivalent to </em>x.<em />

Now, to get the money by using cross multiplication method:

\frac{3}{18} =\frac{6}{x}

<em>By cross multiplying we get"</em>

<em />3x=108<em />

<em>Dividing both sides by 3 we get:</em>

x=36.

<u><em>The money MIles will collect = $36.</em></u>

Therefore,  if Miles sells 6 tickets the money he will collect is $36.

5 0
3 years ago
Which of the scatterplots to the right show ​a) no​ association? ​b) a negative​ association? ​c) a linear​ association? ​d) a w
Len [333]

Answer:

A scatter plot to the right shows  a very strong​ association.

Step-by-step explanation:

Because  a scatter plot to the right shows that both variables are positive and they both increase, so it shows a strong association between those variables.

4 0
3 years ago
A line passes through the point (-8, 6) and has a slope of -5/4.
Margarita [4]

Answer:

y = -5/4x - 4

Step-by-step explanation:

Plug in 6 for y and -8 for x. Then solve for b or "y-intercept". You should get -4

5 0
2 years ago
Read 2 more answers
Brigid is picking strawberries at the Pick-Your-Own Farm. Her goal is to pick 5 bushels of strawberries. She has already picked
Dafna11 [192]
This question does not make much sense. Brigid has already picked 112 bushels, and she picks at a rate of 58 bushels per hour, the scenario question does not make any sense. 58h + 112 = 5...? What does this mean? But whatever the left side of the equation is, first subtract 112 from both sides and divide by 58, then you will get the value of "h."
8 0
3 years ago
Read 2 more answers
Other questions:
  • im too lazy to answer my sister questions (its easy but I got something else to do) do all multiplication all way to 12
    14·2 answers
  • its the end of the school year and a tenth grade civics class is planning a barbecue to celebrate. the class has drinks and dess
    8·1 answer
  • The Jurassic zoo charges $10 for each adult admission and $2 for each child. The total bill for 182 people from a school trip wa
    13·1 answer
  • Last one was blurry . Please help again thanks !
    13·1 answer
  • The sum of 86, 68, and 38 is 192. What else do you know about the sum of 68, 38, and 86?
    9·1 answer
  • I need help on this question :(
    6·2 answers
  • Solve each inequality below and illustrate the solution on a number line.
    14·2 answers
  • Please can anyone help?
    7·1 answer
  • Uh do yall know the coordinates im supposed to put for the last one
    6·2 answers
  • Help, I don't understand<br><br>ASAP NOW<br><br><br>​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!