Mathematics High School

Express the given in terms of the logarithms of prime numbers:
[tex]log_{4} 405[/tex]
[tex]log_{7}(\frac{8}{81} )[/tex]

Answers

Answer 1

The required expression in terms of logarithm of prim numbers are;

[tex]log_4405=log_4(3^4\times 5)=log_43^3+log_45[/tex]

[tex]log_7(\frac{8}{81} )=log_7(\frac{2^3}{3^4} )=log_72^3-log_73^4[/tex]

Prime numbers are numbers that can only be divisible by 1 and itself.

From the given logarithmic expression, we will need to write 405, 8, and 81 as the product of prime numbers

405 = 3 * 3 * 3 * 3 * 5

405 = 3^4 * 5

8= 2* 2 * 2

8 = 2^3

81 = 3 * 3 * 3 * 3

81 = 3^4

The logarithm expression [tex]log_4405 \ and \ log_7(\frac{8}{81} )[/tex] can be expressed in terms of prime numbers as;

[tex]log_4405=log_4(3^4\times 5)=log_43^3+log_45[/tex]

Similarly;

[tex]log_7(\frac{8}{81} )=log_7(\frac{2^3}{3^4} )=log_72^3-log_73^4[/tex]

Learn more here: https://brainly.com/question/23004769

Related Questions

please I need help solving the equation, -2/5c < 9

Answers

Answer:

c > -22 1/2

Step-by-step explanation:

Step 1: Multiply both sides by -5/2 and flip the sign.

[tex]-\frac{2}{5}c * -\frac{5}{2} < 9 * -\frac{5}{2}[/tex]  [tex]c > -\frac{45}{2}[/tex]  [tex]c > -22\frac{1}{2}[/tex]

Therefore, the answer is c > -22 1/2.

Kyle started a new job part of the way through last month that pays $7 per hour. he began the month making $5 per hour at his old job. kyle worked a total of 54 hours last month and made $338 before deduction. how many hours did he work at his old job?

Answers

Answer:

20hours

Step-by-step explanation:

Old Job hours = 54 -34 = 20 hours

How do you solve this and find x?

Answers

Answer:

fraction form

x= 2 + ln(30)/ln(7)

decimal form

x= 3.74786969

Step-by-step explanation:

What I like to call the logarithmic equation solver.

Bring it down turn it around.

First bring down the 7 to a ㏒7 and the x-2 so that ㏒7(x-2)=30

Then change the constants from on another so then it would look like

㏒7(30)=x-2

solve for x

to solve do the log base finder equation ㏒(30)/ln(7)

and add 2

X is 3.748

To accomplish this task you have to take the logarithm of both sides of the equation to remove the variable from the exponent.

ln(30)/ln(7)+2

ln(30)=3.401

ln(7)=1.946

3.401/1.946=1.7476

1.7476+2=3.748 after considering all extra decimal places to the closest thousandth.

Simplify the expression
8h+​(−7.3d​)−14+5d−3.7h.

Answers


−2.3d+4.3h−14 is the answer .

A bag of grass seed weighs 5.8 pounds. How many pounds would 2.5 bags weigh

Answers

Answer:

Answer: 14.5 pounds

Step-by-step explanation:

Step-by-step explanation: Do 5.8 times 2.5

Answer:

14.5 lb

Step-by-step explanation:

1 bag weighs 5.8 lb.

2.5 bags weight 2.5 × 5.8 lb

2.5 × 5.8 lb = 14.5 lb

Help me Pls

NONSENSE=REPORT
REAL ANSWER=BRAINLIEST+HEART​

Answers

PLACE VALUE. VALUE

6. Hundreds. 200

7. Ones. 1

8. Hundreds. 0

9. Hundreds. 800

10. Tens. 60


don’t mind the 28, i literally have no idea. pls help ^^^ thx <3

Answers

9514 1404 393

Answer:

  (d)  28

Step-by-step explanation:

When you are asked to evaluate g(n) for some value of n, put that value where n is and do the arithmetic.

  g(n) = 3n -2

  g(10) = 3·10 -2

  = 30 -2 = 28

Measure these angles.

a)

b)

Answers

are the angles john cena? cuz i cant see anything

is h correct? someone help

Answers

Answer:

No The correct Answer is "G"

Step-by-step explanation:

First lets find 300% as a number which is 3 ok so now

increase 10 by 300%

so 100%+300%=400%

and half of 400 which is 200%

so H is no correct g is

What is the equation in slope-intercept form for the line that passes through the points
-4,3 and 2,-6 (slope intercept form)​

Answers

Answer:

check the file to see the answer i added a screen shot of the answer

Step-by-step explanation:

solve for x
(4/9)^√x=(2/3)^39-√x

Answers

Answer:

169

Step-by-step explanation:

(4/9)^√x = (2/3)^39-√x

(2/3)^2√x = (2/3)^39-√x

Comparing the bases ,

2√x = 39-√x

3√x = 39

√x = 13

x = 169

Bethany has a mother, 6 sisters, 3 aunts and 2 grandmothers. How many girls are in this family?​

Answers

Answer:

13

Step-by-step explanation:

1 plus 1 plus 6 plus 3 plus 2 equals 13

what is the equation in slope intercept form of the line that has a slope of -7 and y intercept of 3/11

Answers

Answer:

y = -7x + 3/11

Step-by-step explanation:

There were m balloons at the beginning of a party. By the end of the party, 4 of them had popped. Using m, write an expression for the number of balloons that were left. Please help! <3

Answers

Answer:

m - 4

Step-by-step explanation:

So, m amount of balloons at the beginning.

When 4 pop, that means there are 4 less than the beginning.

m - 4

Using the formula find the slope of a line with these two points (2,10) and (5,15).

Answers

Answer:

1.66667

Step-by-step explanation:

using online slope calculater

I forgot how to do this stuff so please help

Answers

Answer:

116 in

Step-by-step explanation:

In order to select new board members, the French club held an election. 70% of the 90 members of the club voted. How many members voted?

Answers

Answer:

63 members.

Step-by-step explanation:

70% of the votes means that every 100 people, 70 went to cast their ballot, or 7 every 10. Now in the club there are 9 groups of 10 people, so 9x7 = 63 people

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!6

Answers

Answer:

parami es el A por q no seria basico las demas la B C y D noloson

I NEED ANSWER ASP PLEASE

Answers

Answer:

n=72x9

Step-by-step explanation:

Because Marley is 9x as much, so that's 72x9.

The answer is D. 72/9 = 8

the coordinates of the point of intersection of lines px + y = 3 and x + 2y = q are (2, -3). find the value of p and q

Answers

Answer:

p = 3 and q = - 4

Step-by-step explanation:

Substitute the coordinates of the solution (2, - 3 ) into the equations and solve for p and q

px + y = 3 , then

2p - 3 = 3 ( add 3 to both sides )

2p = 6 ( divide both sides by 2 )

p = 3

and

x + 2y = q , then

2 + 2(- 3) = q

2 - 6 = q , so

q = - 4

please help me woth this

Answers

What you would want to do is first graph the points it lists to you which are -6,6 and 1,6, remember the first number of the coordinate is X and the second number is Y. The X is on the horizontal line while the Y is vertical. Once you find the general place where the rectangle would go you would have to find the perimeter which is 30. The total perimeter can be found by using the equation P = 2L + 2W which just means the length of a side multiplied by 2 plus the width of a side multiplied by 2 equals the perimeter. I don’t have enough time to answer it fully but you would need to plot the coordinates, then find a place where the rectangle would have a perimeter equal to 30. Good luck on your question.

The given bar graph shows the number of rooms, bathrooms, fireplaces, and elevators in the building.
Combined, there are 199 rooms, bathrooms, fireplaces, and elevators. The number of rooms exceeds the
number of bathrooms and fireplaces by 68. The difference between the number of fireplaces and elevators is
23. If the number of bathrooms is doubled, it exceeds the number of fireplaces and elevators by 47. Determin
the number of rooms, bathrooms, fireplaces, and elevators in the building.

Answers

Using a system of equations, it is found that there are:

132 rooms.38 bathrooms.26 fireplaces.3 elevators.

For the system, we have that:

The number of rooms is x.The number of bathrooms is y.The number of fireplaces is z.The number of elevators is w.

Combined, there are 199 rooms, hence:

[tex]x + y + z + w = 199[/tex]

The number of rooms exceeds the  number of bathrooms and fireplaces by 68, hence:

[tex]x = y + z + 68[/tex]

The difference between the number of fireplaces and elevators is  23, hence:

[tex]z - w = 23[/tex]

If the number of bathrooms is doubled, it exceeds the number of fireplaces and elevators by 47, hence:

[tex]2y = z + w + 47[/tex]

Replacing the third equation into the fourth:

[tex]z = 23 + w[/tex]

[tex]2y = z + w + 47[/tex]

[tex]2y = 23 + w + w + 47[/tex]

[tex]2y = 2w + 70[/tex]

[tex]y = w + 35[/tex]

Then, from the second equation:

[tex]x = y + z + 68[/tex]

[tex]y + z = x - 68[/tex]

We can solve for w, considering that:

[tex]y = w + 35[/tex]

[tex]z = 23 + w[/tex]

[tex]y + z = x - 68[/tex]

[tex]x = y + z + 68[/tex]

[tex]x = w + 35 + w + 23 + 68[/tex]

[tex]x = 2w + 126[/tex]

[tex]x + y + z + w = 199[/tex]

[tex]2w + 126 + w + 35 + 23 + w + w = 199[/tex]

[tex]5w + 184 = 199[/tex]

[tex]5w = 15[/tex]

[tex]w = \frac{15}{5}[/tex]

[tex]w = 3[/tex]

Then, solving for the other variables:

[tex]x = 2w + 126 = 2(3) + 126 = 132[/tex]

[tex]y = w + 35 = 3 + 35 = 38[/tex]

[tex]z = 23 + w = 23 + 3 = 26[/tex]

There are:

132 rooms.38 bathrooms.26 fireplaces.3 elevators.

A similar problem is given at https://brainly.com/question/17096268

Please explain.
No bit links.

Answers

Answer:

Top right

Step-by-step explanation:

The equation is saying that x is greater than or equal to the number two. That mean our line will be bold and not dotted and the the shaded area will be everywhere past the 2 line

Can you give me the answer?

Answers

Answer:

39

Step-by-step explanation:

The inside of a triangle adds up to 180:

90 because that square box is 90 degrees

90+50=141

180-141=39

What is the equation of the line in slope-intercept form?


y = 1/7x-15/7

y = 1/7x+15/7

y = 15/7x-1/7

y = 15/7x+1/7
NEED IT NOW!!

Answers

Answer:

B IS THE ANSWER

Step-by-step explanation:

I thought of a 2 digit number. The digits of my number are different. The unit digit of my number is the tens digit raised theird power. What is my number?

Answers

Answer:

Step-by-step explanation:

I thought of a 2 digit number. The digits of my number are different:  [XY]

Then I'm lost. Does "The unit digit of my number is the tens digit raised third power" mean that the X is raised to the third power?:

X^3

But then we need more information.  X could be 1, 2,3, or 4.  At 5 it becomes a three digit number.  All of the other option result in a two digit number with different digits, so all seem possible.  I don't know how to answer this without more information.

Which set of ordered pairs does not represent a function?
a
O{(-6, -9), (-2, -3), (–9,2), (2, -3)}
O {(-2,0), (-5,8), (7,9), (6,8)}
O {(6,9), (-7,8), (1, –4), (8,8)}
O{(-2, -6), (-1,2), (-2, – 7), (6,6)}
Submit Answer

Answers

Answer:

Option 4: {(-2, -6), (-1,2), (-2, – 7), (6,6)}

Step-by-step explanation:

Definitions:A function is a relation for which no two ordered pairs have the same first component (or x-values) and different second component (y-values). The set of first components is the input, also referred as the domain. The set of second components is the output, also referred as the range.

In order to determine whether a given relation is a function, one must always take notice of the x-values ⇒ make sure that an x-value does not have more than one corresponding y-value.

Solution:

Option 1:  {(-6, -9), (-2, -3), (–9,2), (2, -3)}  ⇒ This relation is a function. Each input has one corresponding output.

Option 2: {(-2,0), (-5,8), (7,9), (6,8)}   ⇒ This relation is also a function. Each input has one corresponding output.

Option 3: {(6,9), (-7,8), (1, –4), (8,8)}  ⇒ This relation is also a function. Each input has one corresponding output.

Option 4:  {(-2, -6), (-1,2), (-2, – 7), (6,6)} ⇒ This relation is not a function. The x-value, x = -2, has two corresponding y-values: y = -6, and y = -7.

Therefore, the correct answer is Option 4: {(-2, -6), (-1,2), (-2, – 7), (6,6)}.

Answer:

the last one {(-2, -6), (-1,2), (-2, – 7), (6,6)}

Step-by-step explanation:

it has 2 of the same x values with 2 different y coordinates, in other words it fails the vertical line test.

If the point (2K-3, K+2) lies on the graph of the equation 2x+y+14=0, find the value of k.?​

Answers

Answer:

k = -2

Step-by-step explanation:

Substitute 2k-3 for x and k+2 for 2

2x + y + 14 =0

2(2k-3) + (k + 2) + 14 = 0

4k - 6 + k + 2 + 14 = 0

4k + k - 6 + 2 + 14 = 0

5k + 10 = 0

5k + 10 - 10 = 0 - 10

5k = -10

[tex]\frac{5k}{5} = \frac{-10}{5}[/tex]

k = -2

Amir posts a video trailer

Answers

Step-by-step explanation:

He gets five positive reviews

Help please please urgently

Answers

Answer:

I think the answer to the question is 3/10?

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