Please Help! I will give brainliest! <3

Given <br><img src="https://tex.z-dn.net/?f=%20log_%7B2%7D%28x%29%20%20%3D%20%20%5Cfrac%7B3%7D%7B%20log_%7Bxy%7D%282%29%20%7D%20

Naily [24]

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:

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

7 0

3 years ago

Foot pieces you can cut from 5 feet of

Rzqust [24]

Answer:

1p = r

Step-by-step explanation:

You are asking how many 1-foot pieces you can make out of a 5 foot piece of ribbon. You are asking for an equation.

p = the # of pieces

r = the amount of ribbon

So lets try the equation:

1p = r

1(4) = r

1*4 = 4

4 = r

<h2><u>PLEASE MARK BRAINLIEST! </u></h2>

7 0

3 years ago

Combine as indicated by the signs. 8-y/3y + y+2/9y - 2/6y

Taya2010 [7]

Answer:

26 + y

----------

9y

Step-by-step explanation:

Your using parentheses here would remove a great deal of ambiguity. Looking at your 8-y/3y + y+2/9y - 2/6y, I have interpreted it to mean:

(8-y)/3y + (y+2)/9y - (2/6)y. For example, without parentheses, your 8-y/3y might be interpreted differently, as 8 - y/(3y), or 8 - 1/3.

Looking at (8-y)/3y + (y+2)/9y - (2/6)y again, we see three different denominators: 3y, 9y and 6 y. The LCD here is 9y. Multiplying all three terms of (8-y)/3y + (y+2)/9y - (2/6)y by the LCD, we get:

3(8-y) + (y+2) + 3y. We must now divide this by the LCD:

3(8-y) + (y+2) + 3y

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

9y

Next we need to perform the indicated multiplication:

24 - 3y + y + 2 + 3y

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

9y

and then to combine like terms:

24 + 2 - 3y + y + 3y, 26 + y

---------------------------- or -----------

9y 9y

7 0

3 years ago

Read 2 more answers

Complete each calculation using the distributive property.

Alisiya [41]

What are the answer options?

7 0

3 years ago

100 point reward with certified answer. 4 basic algebra questions, must show work. If the answers are wrong your response will b

ipn [44]

Y=kx
12=-4k
k = -3

so when y = 15
y = kx
15 = -3x
x = -5

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

$50 / 0.04 = $1250 (4% interest)

so
1250 * 0.06 = $75

answer
interest $75 at 6%

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

y = kx
1/4 = 4k
k = 1/16

when x = 5
y = kx
y = 1/16(5)
y = 5/16

-----------
y = kx
-5 = 4k
k = -5/4

direct equation
y = -5/4x

6 0

3 years ago