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
Mila [183]
3 years ago
13

Given

" id="TexFormula1" title=" log_{2}(x) = \frac{3}{ log_{xy}(2) } " alt=" log_{2}(x) = \frac{3}{ log_{xy}(2) } " align="absmiddle" class="latex-formula">
express y in terms of x​
Mathematics
1 answer:
Naily [24]3 years ago
7 0

Answer:

\displaystyle y = x^{-\frac{2}{3}}

Step-by-step explanation:

<u>Logarithms</u>

Some properties of logarithms will be useful to solve this problem:

1. \log(pq)=\log p+\log q

2. \displaystyle \log_pq=\frac{1}{\log_qp}

3. \displaystyle \log p^q=q\log p

We are given the equation:

\displaystyle \log_{2}(x) = \frac{3}{ \log_{xy}(2) }

Applying the second property:

\displaystyle  \log_{xy}(2)=\frac{1}{ \log_{2}(xy)}

Substituting:

\displaystyle \log_{2}(x) = 3\log_{2}(xy)

Applying the first property:

\displaystyle \log_{2}(x) = 3(\log_{2}(x)+\log_{2}(y))

Operating:

\displaystyle \log_{2}(x) = 3\log_{2}(x)+3\log_{2}(y)

Rearranging:

\displaystyle \log_{2}(x) - 3\log_{2}(x)=3\log_{2}(y)

Simplifying:

\displaystyle -2\log_{2}(x) =3\log_{2}(y)

Dividing by 3:

\displaystyle \log_{2}(y)=\frac{-2\log_{2}(x)}{3}

Applying the third property:

\displaystyle \log_{2}(y)=\log_{2}\left(x^{-\frac{2}{3}}\right)

Applying inverse logs:

\boxed{y = x^{-\frac{2}{3}}}

You might be interested in
Write perimeter and area of circle​
alexira [117]

Answer:

The perimeter of a circle is π × d. Here's is the diameter of the circle. Hence, the perimeter of a circle is half of that of the circle that is ½ π × d.

The area of a circle is pi times the radius squared (A = π r²). Learn how to use this formula to find the area of a circle when given the diameter.

Step-by-step explanation:

8 0
3 years ago
The cities Cleveland, Ohio; Erie, Pennsylvania; and Rochester, New York, in respective order, lie approximately in a straight li
Ann [662]

Answer:

  Erie to Rochester is 145 miles

Step-by-step explanation:

If we designate the points of interest as C, E, and R, we are told that ...

  CE + ER = CR . . . . . the various distances are segments of a straight line

For CE = 94 and CR = 239, we can fill in the given information and solve for ER.

  94 + ER = 239

  ER = 239 -94 . . . . . . subtract 94 from both sides of the equation

  ER = 145

The distance from Erie to Rochester is 145 miles.

7 0
3 years ago
Create and solve a system of equations for the following scenario: Luke and Leia are selling hot dogs and hamburgers at a minor
mixas84 [53]

So x + y = 45, and 4x + 5y = 195. Get y by itself. Subtract x from both sides in the first equation to get y = 45 -x, and subtract 4x from the second equation to get 5y = 195 - 4x. Divide by 5 to both sides to get y = 39 - 4/5x. 39 - 4/5x = 45 - x. Add x to both sides to get 39 - 1/5x = 45. Subtract 39 from both sides to get -1/5x = 6. Divide by -1/5 to get x = -30, or 30. In the first equation, do 30 + y = 45. Subtract 30 from both sides to get y = 15. Check. 4(30) + 15(5) = 195, or 120 + 75 = 195.


5 0
3 years ago
Pls help<br> will mark brainliest
yanalaym [24]

Answer:

1.93433

Step-by-step explanation:

Since all triangles have an interior angle sum of 180, the second angle is 45. this also means that x and y are equal. Using the pythagorean theorem, we can produce the equation 2\sqrt{14} = 2x^2. dividing both sides by two we get x^2= \sqrt{14}. when we take the square root of root 14 we get 1.934335

4 0
3 years ago
Two kilos of taronges and three kilos of mandarins cost 11.50 euros. Three kilos of taronges and two of mandarins cost 11 euros.
Illusion [34]

Answer:

Hence the pricing for each product will be taronges with 2 euros and mandarins with 2.5 euros.

Step-by-step explanation:

Given:

2 kg of taronges and 3 kg mandarins cost 11.5 euros

3kg taronges and 2 kg mandarins cost 11 euros

To Find:

Price for each product

Solution:

<em>Consider </em>

<em>Taronges =x euros</em>

<em>Mandarins=y euros</em>

So by given condition,

2x+3y=11.5  ....................equation(1)

and 3x+2y=11 ..............equation (2)

So , using substitution method,

3x=11-2y

x=11-2y/3 .......equation (3)

Using above value in equation(1) we get ,

2(11-2y)/3+3y=11.5

y=(11.5*3-22)/5)

y=2.5 euros

Using above value in equation(3)  we get ,

x=(11-2y)/3

x=(11-2*2.5)/3

x=(11-5)/3

x=2 euros

5 0
3 years ago
Other questions:
  • Twenty one is no less than the sum of a number and -2
    8·1 answer
  • You but 125 tickets to an amusement park the each cost $19.50. What is the total cost of the 125 tickets
    15·1 answer
  • Mr George has $59.75 in his bank account, but then he bought some new ties and some pancakes. After the purchase, he was in debt
    5·1 answer
  • HELP!!!!!!!!! THIS IS DUE TOMMOROW!!!!!
    5·1 answer
  • Evaluate the problem -3-(+4)
    9·2 answers
  • the french club is sponsoring a bake sale. if their goal is to raise at least $135, how many pastries must they sell at $3.00 ea
    11·2 answers
  • Help please urgenttt
    10·1 answer
  • A butterfly can fly 82 feet in four seconds and a dragonfly 50 in two seconds. which is faster
    13·1 answer
  • Charlie guesses that his dog weighs 34. 5 pounds. The dog actually weighs 32. 7 pounds. What is the percent error in Charlie’s g
    14·1 answer
  • Find the slope of the line.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!