Using the change-of-base formula, which of the following is equivalent to the
logarithmic expression below?
log, 18

Using The Change-of-base Formula, Which Of The Following Is Equivalent To Thelogarithmic Expression Below?log,

Answers

Answer 1

Given:

The logarithmic expression is:

[tex]\log_718[/tex]

To find:

The equivalent expression of given expression by using change-of-base formula.

Solution:

The change-of-base formula is:

[tex]\log_ba=\dfrac{\log_ca}{\log_cb}[/tex]

The given expression is:

[tex]\log_718[/tex]

Using the change-of-base formula, we get

[tex]\log_718=\dfrac{\log_c18}{\log_c7}[/tex]

Where, is a constant and c>0.

Let [tex]c=10[/tex], then

[tex]\log_718=\dfrac{\log_{10}18}{\log_{10}7}[/tex]

Therefore, the correct option is a.


Related Questions

On the same day, Parker’s friend, Peggy, was charged $5 for 1 1/2 lb. of gummy candy. Explain in terms of the graph why this must be a mistake.

Answers

Answer:

After a quick online search, I've found that the complete question is:

a) Parker paid $4.50 for three pounds of gummy candy. Assuming each pound of gummy candy costs  the same amount, complete the table of values representing the cost of gummy candy in pounds.

Then we want to graph the points, and then comes our question:

c) On the same day, Parker’s friend, Peggy, was charged $5 for 1 1/2 lb. of gummy candy. Explain in terms of the graph why this must be a mistake.

So first, we know that this is a proportional relationship (each pound of candy costs the same)

And 0 pounds of candy should cost $0.

Then the relation between y (price) and x (number of lb) is:

y = k*lb

where k is the cost per lb.

Knowing that Parker paid $4.50 for three pounds of gummy candy, the relation is:

$4.50 = k*3lb

($4.50/3lb) = k = $1.50/lb

Then the linear relation is:

y = ($1.50/lb)*x

Now, in this question we can see that Parker's friend was charged $5 for ( 1 and 1/2) lb of candy.

If we replace those values in the equation, we get:

$5 = ($1.50/lb)*(1 + 1/2)lb = $2.25

This equation is false, then, in terms of the graph, the point ( (1 and 1/2)lb, $5) does not belong on the graph that you found in the previous points.

pls help me out here! ty in advance!!

Answers

Answer:

the value for x=50

Step-by-step explanation:

180=74+56+x

180=130+x

x=50

A bag contains 20 candies: 9 pink candies, 8 red candies, and the rest green candies. Without looking, Sarah pulls out a piece of candy. What is the probability of Sarah pulling out a green candy what is heat transfer?


( A) 1/10
( B) 3/10
(C) 3/20
(D) 1/20

Answers

Answer:

The answer is C

Hope this helps!

Mark me brainliest if I'm right ;)

Melissa has 120 vanilla cake pops to sell. Each vanilla cake pops is covered with one topping. 1/2 ​ of the cake pops are covered with chocolate sprinkles. 1/3​ of the cake pops are covered with strawberry sprinkles. * the rest are covered with green sprinkles. How many cake pops are covered with green sprinkles?

Answers

Answer:

The Answer is 20 cake pops are covered with green sprinkles.

Step-by-step explanation:

So if you have 1/2 choclate, 1/3 strawberry, and the rest are green, you first need to convert the Chocolate and the Strawberry into the same fraction. As shown:

Chocolate: 1/2=3/6

Strawberry:1/3=2/6

The rest are Green sprinkles.

So, your equation would be:

Chocolate sprinkles + Strawberry Sprinkles + Green Sprinkles = Total

And their are 5/6 of Chocolate and Strawberry Sprinkles...

That would mean 100 Chocolate and Strawberry Sprinkles!

Because 1/6 of 120 is 20 and multiply that by five and you have 100...

Now that we have that, and we know the rest are green...

we just do 120-100=20

So their you go!

Sorry its long but hope it helps! <3

Rachel rolls two number cubes, each with sides that are labeled 1 to 6. What is the probability that one number cube lands on a 1 and the other lands on an even?

Answers

Answer:

4/6. out of 1 2 3 4 5 6 only 3 number are even.but it says lands on 1 and the other lands on even. so 3 +1 = 4. sorry if it doesnt make sense

the area of a rectangle is x^2 - 13x + 30 find the dimensions and area of the rectangle of the perimeter is 30

Answers

Answer:

The area and perimeter of a rectangle work with steps shows the complete step-by-step calculation for finding the perimeter, area and diagonal length of the rectangle with the length of 5 in 5 i n and the width of 10 in 10 i n using the perimeter, area and diagonal length formulas.

Step-by-step explanation:

plz help me illl give brainlist 5.0 and thanks plz help rn !!!

Answers

Answer:

4+4+1

Step-by-step explanation:

Answer:

4 + 4 + 1

Step-by-step explanation:

4 + 4 + 1 = 9

4 + 5 = 9

They both equal up to 9

A straw is placed inside a rectangular box that is 2" x 6" x 8". If the straw fits exactly into the box diagonally from the bottom left corner into the top right back corner how long is the straw?

Answers

Answer: [tex]10.2"[/tex]

Step-by-step explanation:

Given

The dimension of the rectangular box is [tex]2"\times 6"\times8"[/tex]

If the Straw  fits exactly into the box diagonally

So, the length of the longest diagonal of the rectangular box is equal to the length of the straw i.e.

[tex]\Rightarrow l=\sqrt{2^2+6^2+8^2}\\\\\Rightarrow l=\sqrt{4+36+64}\\\\\Rightarrow l=\sqrt{104}\\\Rightarrow l=10.19\approx 10.2"[/tex]

Cody purchased a car for $4500 that will depreciate 28% a year. Write an exponential growth/decay equation that represents the value of Cody's car overtime. How much will the car be worth in 15 years? Round to the nearest cent.

Answers

Answer:

$32.60

Step-by-step explanation:

This question has to to do with exponential decay. The formula is given as:

y = a(1 - r)^x

y = Value of the material after x years

a = Initial value of the material

x = Time in years

r = rate of depreciation or decay

Therefore,

y = 4500 × (1 - 0.28)¹⁵

y = 4500 × 0.72¹⁵

y = $32.598675906

y = Approximately = $32.60

Therefore the of the car after 15 years = $32.60

Mr. Bates and Mr. Z want to refinish the community center gym floor. The rectangular floor is 15.2 m wide and 25.6 long. If each gallon of polyurethane covers about 180 square meters, how many gallons should Mr. Bates and Mr. Z buy? *

Answers

Answer:

3 gallons

Step-by-step explanation:

area = 15.2 x 25.6 = 389.12 m²

389.12/180 = 2.16

Find the Volume (look at the picture)

Answers

Answer:

V ≈ 263.9 units³

Step-by-step explanation:

The volume (V) of a cone is calculated as

V = [tex]\frac{1}{3}[/tex] πr²h ( r is the radius and h the height )

Here r = 6 and h = 7 , then

V = [tex]\frac{1}{3}[/tex] π × 6² × 7

   = [tex]\frac{1}{3}[/tex]π × 36 × 7

   = [tex]\frac{1}{3}[/tex]π × 252

   = 84 π

   ≈ 263.9 units³ ( to 1 dec. place )

Translate the expression: 3 times the difference between 7 and
g is 90

Answers

Answer:

3(7-g)=90

You multiply the expression by 3. The difference means to subtract two values. The whole equation equals 90.

Below. What is m∠1?

m∠1 =

Answers

Answer:

m∠1 = 70°

Step-by-step explanation:

Step 1

Sum of angles on a straight line = 180°

Hence:

180° - 101°

= 79°

Sum of interior angles in a triangle = 180°

Therefore,

m∠1 = 180° - (79 ° + 31°)

m∠1 = 180° - 110°

m∠1 = 70°

Which equation best represents the relationship between x and y in the graph?
A. y = 3x + 3
B. y = x + 3
C. y = 3x - 1
D. y = 13 - 1


15 points pls I need ASAP

Answers

Answer:

A. y = 3x + 3

Step-by-step explanation:

y=mx+b

b is the y-intercept (0,y) so lets start with that

We can see that the line touches 3 on the y intercept to get (0,3) meaning b=3

For the slope (m) I like to count rise over run so if we start from (0,3) and go up 3 over 1 we get 3/1 or 3 for m

The whole equation is y=3x+3

the answer is A because the first intercept would be at positive three

Find the volume of the prism

Answers

Answer:

Step-by-step explanation:

The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm.

V=Bh the length of the rectangle is 9 cm and the width is 7 cm

The radius of a circle is 2 m. Find the circumference to the nearest tenth.

Answers

Answer:

25.13 or 25.1

Step-by-step explanation:

2 x pi/3.14x4

Answer:

12.6

Step-by-step explanation:

circumference=2πr

=2 x 3.142 x 2

= 12.6 to the nearest tenth

Alaina surveys 75 of her classmates and finds that 48% of them like to eat tacos. She also finds that 60% of her 45 relatives like tacos. How many more
of her classmates like tacos as compared to her relatives?

Answers

Answer:  9 more of her classmates like tacos as compared to her relatives

Step-by-step explanation:

first mutiply 75 x 48 =3600

3600/100=36

Then, 45 x 60=2700

2700/100=27

and substract 36-27=9

thats the answer, hope this helped!

A quality control inspector at a clothing manufacturer

Answers

Quality control inspectors monitor quality standards for nearly all manufactured products, including foods, textiles, clothing, glassware, motor vehicles, electronic components, computers, and structural steel. Specific job duties vary across the wide range of industries in which these inspectors work.

which statement does not describe a normal distribution?
A: The median is equal to the mean
B: The distribution is not symmetric
C: The number of observations trails off as you move away from the mean
D: Most of the observations are near the mean

Answers

Answer:

B.

Step-by-step explanation:

The distribution is symmetric

Answer:

B.  The distribution is not symmetric

Step-by-step explanation:

HELP ASAPUse the table to identify values of p and q that can be used to factor
x2 + x - 12 as (x + p)(x + 4).
P
p +
2.
-2.
9
-6
6
4
3
-1
1
-3
4
A. 2 and -6
B. -3 and 4
C. -2 and 6
D. 3 and -4

Answers

the answer would be b

Option B is correct, the values of p and q in expression are -3 and 4.\

The given expression is x²+x-12.

This is expressed as (x+p)(x+q)

We have to find the values of p and q.

x²+x-12

Let us factorize the expression:

x²+4x-3x-12

x(x+4)-3(x+4)

(x-3)(x+4)

When we compare this with (x+p)(x+q) we get:

p=-3 and q=4

Hence, the values of p and q in expression are -3 and 4.

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ7

What is 5 to the 6 power divided by 3794.3?

Answers

Answer:

4.11801913396

Step-by-step explanation:

Heart me pls

What are the answer please number which question you are answering

Answers

Answer:

7.

This is a complementary angle, which means that the two angles add up to 90 degrees. The two angles, in this case, are b and 52. Thus, we have:

b + 52 = 90

b = 38.

Therefore, b is 38 degrees.

8. This is a supplementary angle, which means that the two angles add up to 180 degrees. There is a right angle in the picture to confuse us, so we can just pretend that that doesn't exist, and just focus on the 180-degree angle (which is the straight line). The two angles shown are b and 117, so we have:

b + 117 = 180

b = 63

Therefore, b is 63 degrees.

9. This is a supplementary angle, which means that the two angles add up to 180 degrees. There is another line in the picture to confuse us, so we can just pretend that the line that is making a triangle (the one opposite of 125 degrees) doesn't exist, and just focus on the 180-degree angle (which is the straight line). The two angles shown are b and 125, so we have:

b + 125 = 180

b = 55

Therefore, b is 55 degrees.

The green parallelogram is a dilation of the black parallelogram. What is the scale factor of the dilation?
A) 1/3
B) 1/2
C) 2
D) 3

Answers

Answer:  B)  1/2

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

Explanation:

"The green parallelogram is a dilation of the black parallelogram"

This tells us that the preimage is the black parallelogram and the image is the green one.

In short, the mapping is [tex]\text{black} \to \text{green}[/tex]

The image is smaller than the preimage (green is smaller than black), indicating the scale factor is some value of k such that 0 < k < 1. We can rule out choices C and D because of this.

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

Measuring along the top, we can see that the black parallelogram goes from x = -6 to x = 8. Check out the image shown below where I've marked your given diagram, adding on helpful lines to show this going on.

The number-line distance from x = -6 to x = 8 is 14 units, so the top side of the black parallelogram is 14 units long.

The corresponding top side of the green parallelogram is 7 units long (because it spans from x = -3 and x = 4; as shown in blue in the figure below).

Divide the image length over its corresponding preimage length to get the scale factor.

scale factor = (image length)/(preimage length)

scale factor = 7/14

scale factor = 1/2

which points to choice B as our final answer.

Answer:

THE ANSWER IS C)2

Step-by-step explanation:

I GOT IT WRONG CUZ THIS DUDE ABOVE MEEE

(im big mad)

PLEASE HELP
WILL GIVE BRAINLIEST

Answers

Answer:

The answer will be 1.25

Step-by-step explanation:

12 7/12 - 11/1/3 = 1.25

Hope this helps!

answer:
19/12

step-by-step explanation:
make fractions into like terms
1/3 can be 4/12
12 • 12
144 + 7
151/12
11 • 12
132 + 4
136/12
151 - 132
19/12

Find the geometric mean of 16 and 36. Write your answer in simplest form. The geometric mean is​

Answers

Answer:

Step-by-step explanation:

the geo. mean is the nth root of the product of n numbers

Here there are two numbers; geo. mean is the square root of their product

g = √(16 * 36)

g = 4 * 6

g = 24

Geometric mean is the mean which is the average of a set of a product.

The geometric mean of the given numbers is 24.

What is geometric mean?

Geometric mean is the mean which is the average of a set of a product.

It can be given as,

[tex](\prod_{i=1}^{n}x_i)^{1/n}=\sqrt[n]{x_1\times x_2\times x_3...........x_n}[/tex]

Here [tex]x_i[/tex] is the values of the average and [tex]n[/tex] is the number of values.

Given information-

The numbers given in the problem is 16 and 36.

The Geometric mean for the number 16 and 36 has to find out.

Use the above formula to find the geometric mean for the number 16 and 36. Thus,

[tex]\prod=\sqrt{16\times36}[/tex]

[tex]\prod=\sqrt{576}\\\prod=24[/tex]

Hence the geometric mean of the given numbers is 24.

Learn more about the geometric mean here;

https://brainly.com/question/47038

If Amy has 5 apples and she eats 3 how many does she have left?

Answers

Answer:

2 apples.

Step-by-step explanation:

Answer:

She has 2 more apples left!

Step-by-step explanation:

Simple: this is the equation: 5 - 3 = 2!

A bag contains 5 red marbles, 3 green marbles, and 2 blue marbles. If Nathan draws two marbles without replacing them, what is the probability he will draw 2 red marbles?

Answers

Answer:

It would be a 2/9 chance.

Step-by-step explanation:

So to start, the total amount of marbles is 10, as there's 5 red marbles, 3 green marbles, and 2 blue marbles.

With this, in the first draw, there's a 5/10 chance that a red one will be picked since there's 5 reds of the 10 total.

Since the marbles aren't put back, if a red's chosen in the first draw, it wouldn't be there in the second draw. Therefore in the second draw, there would be 4 reds and 9 in total.

With this, in the second draw, there's a 4/9 chance that a red one will be picked since there's 4 reds of the 9 total.

Now, combine these two probablities by multipliying them and you've got your answer!

5/10 * 4/9 = 20/90 ---> 2/9

Use the Multiplication Law of Exponents to solve the expression below. 91/2.91/2=​

Answers

Answer: 15.64

Step-by-step explanation:

kahn

Alonzo runs each lap in 6 minutes. He will run at most 30 minutes today. What are the possible numbers of laps he will run today?

Use n for the number of laps he will run today.
Write your answer as an inequality solved for n.

Answers

Answer:

N= 5

Step-by-step explanation:

30 ÷ 6 = n

n = 5

30 ÷ 6 = 5

Hope this helps!!

Will mark brainliest!
Find the Volume of the Sphere. Use 3.14 for pi. Round your answer to the nearest whole number.

Answers

Answer:

It is 14130 mm^3

Step-by-step explanation:

So the equation for the volume of a sphere is (4/3) (3.14) r^3. So since we already have the radius, we just plug it in to get the answer:

(4/3) (3.14) r^3

(4/3) (3.14) 15^3

(4/3) (3.14) 3375

(4/3) (10597.5)

14130 mm^3

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