Expand the following logarithm:
[tex] log_{5}( \frac{ {x}^{2} }{y} )^{6} [/tex]

Answers

Answer 1

Answer:

[tex] \displaystyle 12 \log_{5}( {x}^{} {)}^{} - 6 \log_{5}(y ^{} )[/tex]

Step-by-step explanation:

we would like to expand the following

[tex] \displaystyle \log_{5}\bigg( \frac{{x}^{2}}{y} \bigg) ^{6} [/tex]

since we have a division of two different variable we can consider using division logarithm rule

[tex] \displaystyle \log_{5}( {x}^{2} {)}^{6} - \log_{5}(y) ^{6} [/tex]

use law of exponent:

[tex] \displaystyle \log_{5}( {x}^{12} {)}^{} - \log_{5}(y ^{6} )[/tex]

by exponent logarithm rule we acquire:

[tex] \displaystyle 12 \log_{5}( {x}^{} {)}^{} - 6 \log_{5}(y ^{} )[/tex]

and we are done!


Related Questions

In a pack of pretzel sticks, one-quarter of the total number of pretzel sticks is 14.
how many are in the bag

Answers

Answer:

6 lol have  a good day

Answer:

I got 56.

Step-by-step explanation:

Well if 1/4 of the bag is 14, then multiply it by 4. Sorry if this is wrong!

Jim was thinking of a number. Jim doubles it, then adds 19 to get an answer of 70.1. What was the original number?

Answers

Answer:

25.55

Step-by-step explanation:

Let us take the number he thinked of be x .

On doubling it :-

→ N = 2x

On adding 19 :-

→ N = 2x + 19

According to Question :-

→ 2x + 19 = 70.1

→ 2x = 70.1 - 19

→ 2x = 51.1

→ x = 51.1/2

x = 25.55

Hence the required answer is 25.55

For the data that are shown on the graph below, which best describes within which range of x-values extrapolation occurs? On a graph, points are at (0, 15), (1, 17), (3, 18), (4, 20) and (6, 22). x greater-than 6 x less-than 0 and x greater-than 6 x less-than 0 and x greater-than 10 x greater-than-or-equal-to 0 and x less-than-or-equal-to 6 Mark this and return

Answers

Given:

On a graph, points are at (0, 15), (1, 17), (3, 18), (4, 20) and (6, 22).

To find:

The range of x-values extrapolation occurs.

Solution:

Consider the below figure attached with this question.

From the graph or given points it is clear that the x-values are 0, 1, 3, 4, 6.

It means the x-values are from 0 to 6.

So, the range of the x-values is [tex]x\geq 0[/tex] or [tex]x\leq 6[/tex].

The required compound inequality for the range of x-values is [tex]0\leq x\leq 6[/tex].

Therefore, the correct option is D.

Answer:

The answer is B

The perimeter of a certain square is 4 yards. Find the area of the square in square feet.

Please someone help

Answers

Step-by-step explanation:

Write what you know

A square has 4 sides

the perimeter is the sum of the length of all 4 sides

so 4yards / 4 sides = 1 yard per side

we also know a square has all equal sides

that means our area formula will be 1 x 1

12 perimeter 16 area

Little help, please thank you

Answers

Answer:

Finding volume:

2^2 = 4

4 x 3.14 = 12.56

12.56  x 8(height) = 100.48

100.48 divided by 3 ( x 1/3 ) =  around 33.49 in3 is your answer.

If the options dont give you 33.49 just go by 33.51 cubic meters.

Natasha and Richard are marking exam papers. Each set takes Natasha 45 minutes and
Richard 1 hour. Express the times Natasha and Richard take as a ratio.
Give your answer in its simplest form.​

Answers

Answer:

4:3 Natasha is 3 and Richard is 4.

Step-by-step explanation:

60/45=4/3

Please help and show work!

Answers

Answer:

x = 3

Step-by-step explanation:

Two triangles are similar

x/(x+3) = 4/8 cross multiply expressions

8x = 4x + 12

8x - 4x = 12

4x = 12 divide both sides by 4

x = 3

Henry wants to buy a coat that has an original price of $125. During an upcoming sale, the price of the coat will be reduced by 4% each week. Henry plans to wait until the price of the costess than 100 and
uses this inequality to determine w, the number of weeks that he needs to wait to buy the coat
125(0.96)" < 100
How many weeks must Henry wait for the price of the coat to first fall below $100?
AO6
BO5
c.03
DO7

Answers

ANSWER: Here is the link where I answered this question

https://brainly.com/question/23634590?answering=true&answeringSource=feedPublic%2FhomePage%2F1

Find lawn area in m^2

Answers

Answer:

area of lawn = 15.708 square meters

Step-by-step explanation:

pi 3 squared (area of lawn and flower bed) - pi 2 squared (area of flower bed)= area of lawn

PLEASE HELP!!! 20 pts and BRAINLY if you show steps

Amanda graphed line m and line n on a coordinate plane, as shown below.

Which of the following statements is true?
A. The slope of line m is greater then the slope of line n
B. The slope of line n is greater than the slope of line m
C. The x-intercept of line m is greater then the x -intercept of line n
D. The y-intercept of line n is greater then the y -intercept of line m.

Answers

Answer:

B

Step-by-step explanation:

To find the slope of the line, we do y2-y1/x2-x1. In this case, for line n, I used the points (0,0) and (1,2). This means the slope will be 2-0/1-0. Simplify this to get 2/1 or 2. Therefore the slope for line n is 2.

To find the slope of the line, we do y2-y1/x2-x1. In this case, for line m, I used the points (0,7) and (1,8). This means the slope will be 8-7/1-0. This will make the slope 1/1 or 1. Therefore, the slope for m is 1.

Therefore, the slope for line n is greater than the slope of line m.

If this helps please mark as brainliest

which shape has a parallel side choose all the answers

Answers

Answer:

Step-by-step explanation:

it looks like the green four sided one,  has two,   the top and bottom ones, then also the blue four sided one ,  maybe the opposite sides are parallel to each other.  :)  


Please help!!!!!!!!!!!!!

Answers

Plumber a = 60x
Plumber b = 40+55x
An 8 hour job would cost the same for both plumbers. It would cost $480. Plumber a should be hired for a 5 hour job.

List a pair of corresponding angles

Answers

Answer:

2 and 6, 1 and 5, 3 and 7, 4 and 8

Step-by-step explanation:

Any one of those would work

Answer: <1 and <5

Step-by-step explanation:

i need help PLS fr like im dead srs

Answers

Answer:

5/8

Step-by-step explanation:

subtracting 9 From A Certain number gives 13 what is the number​

Answers

Answer:

22

Step-by-step explanation:

N-9=13

N-9+9=13+9

N=22

Answer:

the answer for the question is 22

Step-by-step explanation:

as I said,a certain number =x

therefore,x-9=13

x=13+9

x=22

Which equation models this situation? 26 more than a number is 37.​

Answers

Answer:

x+26=37

Step-by-step explanation:

NEED HELP ASAP PLEASE WILL GIVE BRAINLYEST

Answers

Answer:

a) 1/2

b) 6/100

c)1/4

I'll explain how I got these answers later.

Answer:

Step-by-step explanation:

Total highlighters = 10

A : favourable cases / total cases  = 5/10 = 1/2

B : favourable cases/ total cases * favourable cases/ new total cases

2/10 * 3/9 = 1/5 * 1/3 = 1/15

C : favourable cases/ total cases * favourable cases/ new total cases

5/10 * 4/9 = 1/2 * 4/9 = 4/18

Sin0=20/29 find tan 0

Answers

Answer:

Step-by-step explanation:

here opposite =20, hypotenuse=29

to find adjacent use formula

a^2+b^2=c^2

20^2+b^2=29^2

400+b^2=841

b^2=841-400

b=[tex]\sqrt{441\\}[/tex]

b=21

tan theta=opposite/adjacent

=20/21

therefore tan theta =20/21

Answer:

D. tanθ = 20/21

Step-by-step explanation:

Remember that sinθ = opposite/hypotenuse. In this case, since sinθ = 20/29, we are going to say that opposite = 20 and hypotenuse = 29.

To solve for the adjacent side, use the Pythagorean theorem, a^2 + b^2 = c^2.

When you plug in your values and solve for the other leg, you'll get 21.

Now that we know that the adjacent side/other leg is equal to 21, we can find tanθ, since it's equal to opposite/adjacent.

Opposite = 20

Adjacent = 21

tanθ = 20/21

find the slope between (-3,2) and (-7,-16)

Answers

Answer: The slope between these two is 3.5

Answer:

Solpe=4.5

Step-by-step explanation:

Sorry if I’m wrong, but I think I got it.

So the formula for slope is    y2-y1/x2-x1  

In (-3,-2) )-7,-16),  -3 is x1, -2 is y1, -7 is x2, and -16 is y2.

Now, you need to fill in the formula with these numbers.

-16-2/-7- - 3

-16-2 is -18

-7- - 3 is -4 (two negatives make a positive)

This makes -18/-4. Divide this to get 4.5.

Let me know if you have any questions!! :)

                                       

                                 

is greater than or equal to, minus, 5.

Answers

Answer:

x≥-5

Step-by-step explanation:

x

Sally can run 5 km in 25 minutes. At the same rat of speed, how far can she run in 2 hours and five minutes?

Answers

Answer:

25 km

Step-by-step explanation:

[tex]\frac{5}{25} :\frac{y}{125}[/tex]

y · 25 = 5 · 125

25y = 625

25y ÷ 25 = 625 ÷ 25

y = 25

Round 5,060 to the nearest tenth

Answers

Answer:

5060.0

Step-by-step explanation:

hope this helps with the work

Answer: 5,060
it is already rounded to the nearest tenth! hope that helped :)))

HELP!!! this is graded and no links pls!!!!!!!!

Answers

Answer:

C

Step-by-step explanation:

the answer :
c
self explanation

Write the following number in scientific notation 0.00000407​

Answers

you need to move the decimal so it will be 4.07

Answer:

4.07

Step-by-step explanation:

I am genius


Can someone explain how to do this?

Answers

Answer:

so what you would do is take length time width or 25*25 to find area

Step-by-step explanation:

You need to multiply 25 times 25

Explanation if all four sides are 25 multiplying them is how you get your answer

How many 2/3 of a foot are in 18,491 feet? pls help!!!!!!!!

Answers

Answer:

i round my answer so its 4 but if it wrong its 3

Step-by-step explanation:

Sues dad fixed her play table each of the 4 legs took 2 nails how many nails did he use

Answers

Answer:

8 nails

Step-by-step explanation:

because 4x2=8

Drag each tile to the correct box.
Arrange the matrices in increasing order of their determinant values.

Answers

Answer:

Order of the Matrix will be

[tex]\left[\begin{array}{ccc}6&6\\5&-8\\\end{array}\right][/tex]  

[tex]\left[\begin{array}{ccc}2&4\\5&-5\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}2&6\\3&4\\\end{array}\right][/tex]  

[tex]\left[\begin{array}{ccc}3&2\\4&6\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-2&-7\\5&9\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}2&5\\-2&4\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}4&-3\\5&2\\\end{array}\right][/tex]

Step-by-step explanation:

Given - The matrices are -

[tex]\left[\begin{array}{ccc}2&6\\3&4\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-2&-7\\5&9\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}6&6\\5&-8\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}2&4\\5&-5\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}2&5\\-2&4\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}4&-3\\5&2\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}3&2\\4&6\\\end{array}\right][/tex]

To find - Arrange the matrices in increasing order of their determinant values.

Proof -

Determinant of matrix [tex]\left[\begin{array}{ccc}2&6\\3&4\\\end{array}\right][/tex] is

= (2)(4) - (6)(3)

= 8 - 18

= -10

So,

Determinant of matrix [tex]\left[\begin{array}{ccc}2&6\\3&4\\\end{array}\right][/tex]  = -10

Determinant of matrix [tex]\left[\begin{array}{ccc}-2&-7\\5&9\\\end{array}\right][/tex] is

= (-2)(9) - (-7)(5)

= -18 + 35

= 17

So,

Determinant of matrix [tex]\left[\begin{array}{ccc}-2&-7\\5&9\\\end{array}\right][/tex] = 17

Determinant of matrix [tex]\left[\begin{array}{ccc}6&6\\5&-8\\\end{array}\right][/tex] is

= (6)(-8) - (6)(5)

= -48 - 30

= -78

So,

Determinant of matrix [tex]\left[\begin{array}{ccc}6&6\\5&-8\\\end{array}\right][/tex]  = -78

Determinant of matrix [tex]\left[\begin{array}{ccc}2&4\\5&-5\\\end{array}\right][/tex] is

= (2)(-5) - (4)(5)

= -10 - 20

= -30

So,

Determinant of matrix [tex]\left[\begin{array}{ccc}2&4\\5&-5\\\end{array}\right][/tex] = -30

Determinant of matrix [tex]\left[\begin{array}{ccc}2&5\\-2&4\\\end{array}\right][/tex] is

= (2)(4) - (5)(-2)

= 8 + 10

= 18

So,

Determinant of matrix [tex]\left[\begin{array}{ccc}2&5\\-2&4\\\end{array}\right][/tex] = 18

Determinant of matrix [tex]\left[\begin{array}{ccc}4&-3\\5&2\\\end{array}\right][/tex] is

= (4)(2) - (-3)(5)

= 8 + 15

= 23

So,

Determinant of matrix [tex]\left[\begin{array}{ccc}4&-3\\5&2\\\end{array}\right][/tex]  = 23

Determinant of matrix [tex]\left[\begin{array}{ccc}3&2\\4&6\\\end{array}\right][/tex] is

= (3)(6) - (2)(4)

= 18 - 8

= 10

So,

Determinant of matrix [tex]\left[\begin{array}{ccc}3&2\\4&6\\\end{array}\right][/tex]  = 10

Now,

Increasing order of Determinant is -

-78 < -30 < -10 < 10 < 17 < 18 < 23

So,

Order of the Matrix will be

[tex]\left[\begin{array}{ccc}6&6\\5&-8\\\end{array}\right][/tex]  

[tex]\left[\begin{array}{ccc}2&4\\5&-5\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}2&6\\3&4\\\end{array}\right][/tex]  

[tex]\left[\begin{array}{ccc}3&2\\4&6\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-2&-7\\5&9\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}2&5\\-2&4\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}4&-3\\5&2\\\end{array}\right][/tex]

Answer:

Correct on Edmentum

Step-by-step explanation:

Select all expressions equivalent to 8x - 24.
2(2x - 12)
4(2x - 4)
8(x - 3)
2(4x - 12)

Answers

Answer:

8(x-3)

2(4x-24)

Step-by-step explanation:

You are using the distributive property. Multiply the number outside of the parentheses by each number within the parentheses.

In 8(x-3) = 8x - (8×3) = 8x-24

In 2(4x-12) = (2 × 4x) - (2 × 12) = 8x-24

8(x-3) and 2(4x-12).

Find the value of RT

Answers

Answer:

[tex]RT=7[/tex]

Step-by-step explanation:

[tex]RQ*RP=RS*RT[/tex]

[tex]9*(9+13)=11(11+x)[/tex][tex]9*\frac{22^2}{11} =\frac{11}{11} =(11+x)[/tex][tex]18=11+x[/tex] ⇒ [tex]7[/tex]

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┍━━━━ ⋆⋅☆⋅⋆ ━━━━┑

         hope it helps..

        have a great day!!

┕━━━━ ⋆⋅☆⋅⋆ ━━━━┙

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