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
Find the area of the figure to the nearest hundredth.<br><br>​
marysya [2.9K]

Answer:

51.26 ft

Step-by-step explanation:

First find the area of the triangle:

a=1/2 base times height

a=(1/2)(6)(4)

a=12 ft

Now find the area of the circles:

a= pi times radius squared

a= pi times 2.5 squared

a=19.63 ft

19.63 + 12 = 31.63 ft

5 0
3 years ago
If the filling equipment is functioning properly what is the probability that the volume of oil in a randomly selected barrel wi
Sophie [7]

Answer:

P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)

P(Z>0.8)=1-P(Z\leq 0.8)

P(Z>0.8)=1-0.788=0.212

Step-by-step explanation:

Assuming this previous info : "Trucks carry barrels of crude oil from a port in Texas to a distributer in New Mexico on long  trailers. Filling equipment is used to fill the barrels with the oil. When functioning properly,  the actual volume of oil loaded into each barrel by the filling equipment at the port is  approximately normally distributed with a mean of 55 gallons and a standard deviation of 0.5  gallons. If the mean is greater than 55.4 gallons, the filling mechanism is overfilling."

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the amount filling of a population, and for this case we know the distribution for X is given by:

X \sim N(55,0.5)  

Where \mu=55 and \sigma=0.5

We are interested on this probability

P(X>55.4)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)

And we can find this probability using the complement rule:

P(Z>0.8)=1-P(Z\leq 0.8)

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(Z>0.8)=1-0.788=0.212

8 0
3 years ago
Find the measure for angle DEF
nadezda [96]

Answer:

Step-by-step explanation:

∠DEF=90-58.2=31.8°

4 0
3 years ago
Read 2 more answers
Please help its due today!!<br> Solve for h
antiseptic1488 [7]

Answer:

n= v

------------------

1.047198r2

Step-by-step explanation:

Step 1: Flip the equation.

1.047198nr2=v

Step 2: Divide both sides by 1.047198r^2.

1.047198nr2

1.047198r2

=

v

1.047198r2

n=

v

1.047198r2

8 0
3 years ago
Evaluate the expression below when y = -3.<br><br> 2y + 7<br><br> -4y − 10
Sedbober [7]
1) 1
2) 2

hope this helped :)
4 0
3 years ago
Other questions:
  • Whole numbers are written on cards and then placed in a bag. Tyra selects a single card, writes down the number. and then placed
    7·1 answer
  • Calculate the rectangular prism with a length of 5.6cm, a with of 2.1 cm, and a height of 6.6cm.
    8·1 answer
  • a local restaurant offers a deal if you purchase 3 medium pizza, you get 2 sides dishes for free. if you get a total of 8 side d
    12·1 answer
  • What is the lowest common multiple of 24 &amp; 42
    13·2 answers
  • David invested $1000.ppm what would that money grow to the 18 months at 5.5% interest rate?
    12·1 answer
  • Solve the equation using the zero product principle<br> (x-3)(x+6)=0
    14·1 answer
  • Make x the subject a=7x/k-r
    6·1 answer
  • Pls help me this is my homework
    7·1 answer
  • Four numbers have a mean of 24 Three of the numbers are 22,36 and 9 What is the other number? PLS HELP ME!
    10·1 answer
  • C) How could you use estimation to determine if your answer is reasonable? Explain.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!