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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}}}

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1. Is the product of √16 and 4/7 rational or irrational? Explain your reasoning.
Mandarinka [93]

1) Rational because the square root of 16 is 4 and 4 times 4/7 is a rational number (16/7)

2) Irrational because square root of 684 is irrational C

3) The square root of a is irrational so the answer is irrational. The square root of c is rational so the answer is rational.

4) Jacob is wrong because the square root of 5/7 is irrational so the answer to the problem is irrational.


3 0
3 years ago
Read 2 more answers
How to find the measure of an exterior angle?
MariettaO [177]
180 -internal angel good luck
4 0
3 years ago
What is the x-value of the solution to the system of equations?
ValentinkaMS [17]

Answer:

The solution to the system of equations is:

x=4,\:y=-3

Step-by-step explanation:

Given the system of equations

5x + 4y =8

2x- 3y = 17

solving the system of equations

\begin{bmatrix}5x+4y=8\\ 2x-3y=17\end{bmatrix}

\mathrm{Multiply\:}5x+4y=8\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:10x+8y=16

\mathrm{Multiply\:}2x-3y=17\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:10x-15y=85

\begin{bmatrix}10x+8y=16\\ 10x-15y=85\end{bmatrix}

10x-15y=85

-

\underline{10x+8y=16}

-23y=69

\begin{bmatrix}10x+8y=16\\ -23y=69\end{bmatrix}

solve for y

-23y=69

Divide both sides by -23

\frac{-23y}{-23}=\frac{69}{-23}

y=-3

\mathrm{For\:}10x+8y=16\mathrm{\:plug\:in\:}y=-3

10x+8\left(-3\right)=16

10x-24=16

10x=40

Divide both sides by 10

\frac{10x}{10}=\frac{40}{10}

x=4

Thus, the solution to the system of equations is:

x=4,\:y=-3

7 0
2 years ago
Apply the distributive property to factor out the greatest common factor of all three terms. {10a - 25 + 5b} =10a−25+5b =
Rom4ik [11]

Answer:

5(2a -5 + b)

Step-by-step explanation:

(10a - 25 + 5b) = 5( 2a - 5 + b)

5(b +  2a  - 5) = 5(2a - 5 + b)

8 0
3 years ago
What is 2r - 6r 8 = 40?
Anit [1.1K]
Well first you have to add common like terms in this case 2r and -6r to get -4r now your equation is -4r+8=40, now subtract 8 from both sides to leave r by itself and get -4r=32, now divide both sides by -4 to get r=-8

Hope this helps
3 0
3 years ago
Read 2 more answers
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