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3 years ago

Is 5 a solution of the equation? 13 - d = 8

Mathematics

2 answers:

Goryan [66]3 years ago

8 0

Yes it is write 13-5=8

crimeas [40]3 years ago

3 0

Yes because 13-5=8. not any other single number can be identified in the missing number

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If <img src="https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20x%20%3D%20log_%7Ba%7D%28bc%29" id="TexFormula1" title="\rm \: x = log_{a}(

timama [110]

Use the change-of-basis identity,

$\log_x(y) = \dfrac{\ln(y)}{\ln(x)}$

to write

$xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}$

Use the product-to-sum identity,

$\log_x(yz) = \log_x(y) + \log_x(z)$

to write

$xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}$

Redistribute the factors on the left side as

$xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}$

and simplify to

$xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)$

Now expand the right side:

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}$

Simplify and rewrite using the logarithm properties mentioned earlier.

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1$

$xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}$

$xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}$

$xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)$

$\implies \boxed{xyz = x + y + z + 2}$

(C)

6 0

2 years ago

Use the coordinates of the labeled point to find a point-slope equation of the line.

DerKrebs [107]

Answer:

(-2,-5) (0,-1)

(-1+5)/(0+2)= 4/2= 2

y + 5 = 2(x + 2)

y + 5 = 2x + 4

y = 2x - 1

Step-by-step explanation:

8 0

3 years ago

A product goes from $25 to $27 in price. The product has a percent increase of _____. 7.4% 8% 74% 80%

White raven [17]

8%
27-25 = 2
2/25 = 0.08

5 0

3 years ago

Read 2 more answers

Given: AB is the perpendicular bisector of IK. Name two lengths that are equal.

Paha777 [63]

Since AB is the perpendicular bisector of IK, it separates IK into 2 equal segments. So, the two halves of IK are the same length. (From AB to K, and from AB to I) <span />

5 0

3 years ago

PLEASE HELP ME IVE POSTED THIS 765678 AND STILL NO RESPONSE

Debora [2.8K]

Problem 1

<h3>Answer: 6.7</h3>

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

Work Shown:

The two points are $(x_1,y_1) = (1,-2)$ and $(x_2,y_2) = (4,4)$

Apply the distance formula to get the following

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-4)^2 + (-2-4)^2}\\\\d = \sqrt{(-3)^2 + (-6)^2}\\\\d = \sqrt{9 + 36}\\\\d = \sqrt{45}\\\\d \approx 6.7082039\\\\d \approx 6.7\\\\$

The distance between the two endpoints is roughly 6.7 units. This is the same as saying the segment is roughly 6.7 units long.

======================================================

Problem 2

<h3>Answer: 3.6</h3>

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

Work Shown:

We'll use the distance formula here as well.

This time we have the two points $(x_1,y_1) = (3,1)$ and $(x_2,y_2) = (5,-2)$

The distance between them is...

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-5)^2 + (1-(-2))^2}\\\\d = \sqrt{(3-5)^2 + (1+2)^2}\\\\d = \sqrt{(-2)^2 + (3)^2}\\\\d = \sqrt{4 + 9}\\\\d = \sqrt{13}\\\\d \approx 3.6055513\\\\d \approx 3.6\\\\$

This distance is approximate.

5 0

2 years ago