Solve the equation: 7^n=343

Answers

Answer 1

Answer is

7^n = 7^3

N=3

Answer 2

Answer:

n=3

Step-by-step explanation:

7

n

=343

Use the rules of exponents and logarithms to solve the equation.

7

n

=343

Take the logarithm of both sides of the equation.

log(7

n

)=log(343)

The logarithm of a number raised to a power is the power times the logarithm of the number.

nlog(7)=log(343)

Divide both sides by log(7).

n=

log(7)

log(343)

By the change-of-base formula  

log(b)

log(a)

=log

b

(a).

n=log

7

(343)


Related Questions

What is the value of this expression when a=3 and b= -2? (3a (exponent) -2 b (exponent) 6) exp. -2 ___________________________ (2a (exponent) -1 b (exponent) 5) Its all one equation!

Answers

Answer:

I looked online to find the equation well written, but i could not find it, so i will guess that the equation is:

[tex]\frac{3*a^{-2} - 2*b^{-6}*e^{-2}}{2*a^{-1}*b^{5}}[/tex]

Now we want to find the value of this equation when:

a = 3 and b = -2

So we can just replace these values in the equation, each a is replaced by a 3, and each b is replaced by a -2.

The equation becomes.

[tex]\frac{3*3^{-2} - 2*(-2)^{-6}*e^{-2}}{2*3^{-1}*(-2)^{5}} = 44.3[/tex]

Find an equation for the perpendicular bisector of the line segment whose endpoints are (-9, -1) and (3, – 7).​

Answers

Answer:

y-4=1(x-6) and y= x 10

Step-by-step explanation:

Mr. Boyd completed a 3.19 mile walk/ run. For every 5 minutes of walking, he ran for 1.5 minutes. If he completed his workout in 48:52 minutes, how much of that time was spent running?

Answers

Answer:

He spent 11.25 minutes running

Step-by-step explanation:

Mr. Boyd completed a 3.19 mile walk/ run.

For every 5 minutes of walking, he ran for 1.5 minutes.

He completed his workout in 48.52 minutes.

Hence, we have the equation:

1.5x + 5x = 48.52 minutes

6.5x = 48.52 minutes

x = 48.52/6.5

x = 7.4646153846

Approximately = 7.5 minutes

Therefore the time spent running = 1.5 × 7.5 minutes

= 11.25 mimutes

find the x, if the three angles of an equilateral triangle are 45°, 2x+7°, 45°​

Answers

Answer:

19

Step-by-step explanation:

2x+7=45

2x=38

X=19

I hope this helps

SOMEONE. PLS HELP I ASKED A QUESTION AND I'LL GIVE BRAINLIEST JUST PLS ANSWER IT

Answers

Answer:

Ok, I'll try

Step-by-step explanation:

Dora

Boots

Come on, Dora

Do-do-do-do-Dora (alright)

Do-do-do-do-Dora

Do-do-do-do-Dora

Do-do-do-do-Dora (let's go)

Dora, Dora, Dora the explorer (Dora!)

Boots and super cool Exploradora

Need your help

Grab your backpack, let's go

Jump in, ¡vámonos!

You can lead the way

Hey! Hey!

Do-d-Dora

Do-d-Dora

Do-d-Dora

Do-d-Dora

Swiper no swiping

Swiper no swiping

(Oh, man)

Dora the explorer!

Write a scientific notation in standard form 125.41

Answers

Answer:

1.2541 x^2

Step-by-step explanation:

Lo is leaving from work today at 5:45 p.m. She has errands to run before she meets her friends for dinner at 8 p.m. If it takes Lo of an hour to run each errand, how many errands does she have time to run between work and dinner?

3/4x = 2 1/4

A. 5
B. 3
C. 1
D. 2

Answers

The answer would be B.

Answer:

the answer is B

Step-by-step explanation:

here's why.... 2 times 4 plus 1 is 9 so ... 2 1/4 turns into 9/4 and 3 times 3 is 9 so if u place x with 3 it will be 9/4 therefore the fractions are equal.

NEED HELP ASAP, I WILL GIVE BRAINLIEST

Which diagram shows the parallelogram method for vector addition?

Answers

Answer:

i believe it is c

Step-by-step explanation:

took test on edge

The second picture represents the addition of two vectors u and v by the parallelogram method for vector addition.

What is a vector?

It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.

We have:

Two vectors u and v

The resultant vector will be u + v

As we know, in the parallelogram method for vector addition

We have to place two vectors at the same starting point.

Then complete the parallelogram.

The diagonal of the parallelogram represents the addition of the vector.

Thus, the second picture represents the addition of two vectors u and v by the parallelogram method for vector addition.

Learn more about the vector here:

brainly.com/question/8607618

#SPJ2

which equation represents the same line points as the table

Answers

Answer:

y=-x,A

Step-by-step explanation:

When we input -5 in for x, we get 5

When we input 7 in for x, we get -7

please help, brainliest, five star, thanks

Answers

Answer:

-18+4

Step-by-step explanation:

try to multiply -6 into the (3x-2/3) then I guess you get the answer

Answer:

−18x+4

Step-by-step explanation:

Which of the following is the most likely end for a star that formed from an extremely large nebula? (2 points)

a
Black hole

b
Main sequence

c
Planetary nebula

d
White dwarf

Answers

A star that is formed from an extremely large nebula is most likely to end in a black hole.

Answer:

A black hole

Step-by-step explanation:

take my word for it it is A!

Have a fantastico day!  

Which equation below so that the
8y = -40
y=22
-6x + 8y = -4
-6x + 8y = -40
COMPLETE
The solution to the system Is:

Answers

Answer:

(4 , -5)

Step-by-step explanation:

The sum of three consecutive multiples"
of 8 is 192. Find the multiples.​

Answers

Answer:

7,8,9

Step-by-step explanation:

192/8=24

X+(x+1)+(x+2)=24

3x+3=24

3x=21

x=7

so it’s 7,8,9

the more recent question you asked steps

Apply the fractions formula for multiplication, to

13×45

and solve

1×43×5

=415

Therefore:

13×45=415

Step-by-step explanation:

1) "teacher" wants to build a rectangular dog bowl stand. The top of it will have a perimeter 55 1/2 inches. The length is twice as long as the width. What are the dimensions (length and width) of the top of the dog bowl stand? (Note: Your answer should be in fraction form, not a decimal.) 2) During their basketball game, "teacher 1" shoots twice as many airballs as "teacher 2". "teacher 3" shoots 4 airballs less than "teacher 2". If they shot 24 airballs together, how many airballs did each teacher shoot?

Answers

Answer:

1)

[tex]L=18 \frac{1}{2} in[/tex]

[tex] W= 9 \frac{1}{4} in[/tex]

2)

[tex]T_{1}=14 balls[/tex]

[tex]T_{2}=7 balls[/tex]

[tex]T_{3}=3 balls[/tex]

Step-by-step explanation:

In order to solve this problem, we need to build the equations we need. Since there are two values we want to figure out (length and width) we will then need two equations to solve simultaneously.

First, the problem tells us that the perimeter is 55 1/2 in, which can be rewritten as an improper fraction:

[tex]55 \frac{1}{2}= \frac{55*2+1}{2}= \frac{111}{2}[/tex]

Next, we also know the perimeter of a rectangle is found by using the following formula:

P=2L+2W

where L is the length of the rectangle and W is its width.

So our first equation will look like this:

[tex]2L+2W=\frac{111}{2}[/tex]

Next, the problem tells us that the width of the rectangle is twice its width, so our second equation will look like this:

L=2W

which can be substituted into our first equation:

[tex]2L+L=\frac{111}{2}[/tex]

Now, we can solve this for L, so we get:

[tex]3L=\frac{111}{2}[/tex]

[tex]L=\frac{111}{2*3}[/tex]

[tex]L=\frac{111}{6}=18 \frac{3}{6}=18 \frac{1}{2}[/tex]

so we can now use this information to find its width:

L=2W

[tex] \frac{111}{6}=2W[/tex]

so

[tex]W=\frac{111}{6*2}[/tex]

[tex]W=\frac{111}{12}=9\frac{3}{12}=9\frac{1}{4}[/tex]

2)

When solving this problem it is a good idea to split it into little chunks of information. The first sentence says:

"... "teacher 1" shoots twice as many airballs as "teacher 2"."

This can be translated as an equation like this:

[tex]T_{1}=2T_{2}[/tex]

The next sentence says:

""teacher 3" shoots 4 airballs less than "teacher 2"."

This can be written as an equation like this:

[tex]T_{3}=T_{2}-4[/tex]

and finally, the problem states: "... they shot 24 airballs together,..."

This can be written as an equation like this:

[tex]T_{1}+T_{2}+T_{3}=24[/tex]

so now we can do substitutions. We can take the first and second equations and write them into the third equation so we get:

[tex]2T_{2}+T_{2}+T_{2}-4=24[/tex]

so now we can solve this equation for [tex]T_{2}[/tex], so we get:

[tex]2T_{2}+T_{2}+T_{2}=24+4[/tex]

[tex]4T_{2}=28[/tex]

[tex]T_{2}=\frac{28}{4}[/tex]

[tex]T_{2}=7[/tex]

and once we got this answer, we can find the remaining two answers:

[tex]T_{1}=2T_{2}[/tex]

[tex]T_{1}=2(7)[/tex]

[tex]T_{1}=14[/tex]

and

[tex]T_{3}=T_{2}-4[/tex]

so we get:

[tex]T_{3}=7-4[/tex]

[tex]T_{3}=3[/tex]

Answer:

1)

Step-by-step explanation:

1)

The area of the base of a rectangular prism is 24 square centimeters and the height is 12 centimeters. What is the volume of the rectangular prism in cubic centimeters?

Answers

Answer:

V = 288 cm³

Step-by-step explanation:

Given that,

The area of the base of a rectangular prism is 24 square centimeters and the height is 12 centimeters.

We need to find the volume of the rectangular prism. For a rectangular prism, the volume is given by :

V = lbh

Since, lb = A, area of the prism

V = Ah

V = 24 × 12

= 288 cm³

So, the volume of the rectangular prism is 288 cm³.

tyler's brother earns $12 per hour. the store offers him a raise -a 5% increase per hour . after the raise how much will tyler's brother make per hour

Answers

Answer:

12.50

Step-by-step explanation:

N + 7 < -3 HELPSSS please solve this

Answers

Answer:

n is smaller than -10 so it could be -10, -11, -12 etc.

Step-by-step explanation:

Answer:

n < -10

Step-by-step explanation:

Step 1:  Subtract 7 from both sides.

n+7−7<−3−7, we are left with n<-10

n<−10

Mary is standing out on the balcony of her apartment which is 40 feet above the ground and looks up at a 31° angle to see her friend Sue who is standing on her balcony. If Mary and Sue's apartments are 20 feet apart from one another, how high off the ground is Sue?

Answers

Answer:

52 feet

Step-by-step explanation:

This situation can be represented by the attached figure as in the answer area.

Let M be the location of Mary.

Let S be the location of Sue.

Distance between apartments is given as 20 feet.

Distance between ground and balcony of Mary is 40 feet.

There is a right angled [tex]\triangle MOS[/tex].

[tex]\angle OMS = 31^\circ[/tex]

To find:

The distance SO + 40 feet.

We can use tangent ratio here in right angled [tex]\triangle MOS[/tex].

[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]

[tex]tan31^\circ = \dfrac{SO}{MO}\\\Rightarrow tan31^\circ = \dfrac{SO}{20}\\\Rightarrow SO=20\times 0.6\\\Rightarrow \bold{SO=12\ ft}[/tex]

Height of Sue above ground = 40+12 = 52 feet

PLEASE ANSWER ASAP ASSIGNMENT IS DUE TODAY I WILL MARK BRAINLIST!!!!!!!!!!!!


3. Write an exponential equation for each coin that will give the coin's value, V, at any time, t. Use the formula:
V(t) = P(1 + r)t, where V(t) is the value of the coin in t years, P is the initial investment, and r is the growth rate.
Coin A worth $25 and increase by 7% each year and coin B worth $40 increase by 5% each year

Answers

9514 1404 393

Answer:

V(t) = 25(1.07^t)V(t) = 40(1.05^t)

Step-by-step explanation:

Put the given numbers into the given formula. It can be simplified a little bit.

Formula:

  V(t) = P(1 + r)^t

Coin A

  P = 25, r = .07

  V(t) = 25(1.07^t)

Coin B

  P = 40, r = 0.05

  V(t) = 40(1.05^t)

Someone please help

Answers

-1,-1



Hope this helpppssss

I feel like it's A but i don't know to be honest.

Answers

Answer:

I agree that the answer is A

Step-by-step explanation:

Which number is greater? -|3| or |-3|

Answers

Answer:

there equal

Step-by-step explanation:

There are 6 yellow hexagons 2 red trapezoids and 9 green triangles how many flowers could you make if they were changed 30 yellow hexagons 50 red trapezoids and 60 green triangles. Which shape would you have left over the most

Answers

Answer:

a) 5 flowersb) Trapezoid

Step-by-step explanation:

For one flower, the following shapes are used;

6 yellow hexagons, 2 red trapezoids and 9 green triangles

If we are given 30 yellow hexagons 50 red trapezoids and 60 green triangles, to get the number of flowers we can make, we will find the greatest common factor of 30, 50 and 60

30 = 6*5

50 = (2*5)+40

60 = (9*5)+15

We can see that 5 is common to all the factors. This means that we can make 5 flowers if they were changed to 30 yellow hexagons 50 red trapezoids and 60 green triangles.

Since there are 40 trapezoids left and 15 green triangles left, hence the shape that would have n as left over most is trapezoid (40 left over)

One order of fries costs $1.90. If an order is placed for 6 orders of fries, what will the total cost of the order be? The order will cost___________ dollars. ​

Answers

Answer:

$11.40

Step-by-step explanation:

$1.90*6=$11.40

Subtract 5x2 - 7x - 6 from 9x2 + 3x – 4.

Answers

-7x+4 i’m not sure if it’s correct but i hope it is. sorry if it’s not

2^8 in standard form

Answers

Answer: 256

Step-by-step explanation:

2^8=2*2*2*2*2*2*2*2=256

How do you find the markup rate?

Answers

Answer: Simply take the sales price minus the unit cost, and divide that number by the unit cost. Then, multiply by 100 to determine the markup percentage. For example, if your product costs $50 to make and the selling price is $75, then the markup percentage would be 50%.

Step-by-step explanation:

Answer:

hope this helps!

Step-by-step explanation:

Divide the amount added to the price by the amount the item costs you to buy to find the markup rate expressed as a decimal. In this example, you would divide $2 by $6 to get 0.3333. Convert the markup rate expressed as a decimal to a markup rate expressed as a percentage by multiplying it by 100.

A colony of amoebas is being studied. The mass of the
colony triples every day. On Day x of the study, the
colony has a mass of 3^x mg.
a. What is the mass of the colony on Days 3, 2, and 1?
What is the mass of the colony on Day 0, when the
study begins? Show your work.

Answers

Answer:

Multiply the start amount of the insects by 3 and then by the amount of days

What's the domain of this function graph?
A) (-♾, 0)
B) (0,♾)
C) (-♾,♾)
D) (1,♾)

Answers

Answer:

b) (0,infinity)

Step-by-step explanation:

You can look at the graph and see it starts when x=1, and continues forever in the positive direction.

B because infinity I think

Solve for x, y, and a.

Answers

Answer:

Step-by-step explanation:

x = 55

y = 60

a = 14

did it in my copy but it took too long to upload so i gave up. sry

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