if a^x=b^y and a^y=b^x, show that x=y.​

Answers

Answer 1

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]

Let's solve ~

Using first equation we get,

[tex] {a}^{x} = {b}^{y} [/tex]

[tex]a = \sqrt[x]{ {b}^{y} } [/tex]

[tex]a = {b}^{ \frac{y}{x} } [/tex]

now, plug the value of a in other equation ~

[tex]a {}^{y} = b {}^{x} [/tex]

[tex]( {b}^{ \frac{y}{x} } ) {}^{y} = {b}^{x} [/tex]

[tex]{(b) }^{ \frac{y}{x} \times y} = {b}^{x} [/tex]

[tex] {(b)}^{ \frac{ {y}^{2} }{x} } = {b}^{x} [/tex]

[tex] \dfrac{ {y}^{2} }{x} = x[/tex]

[tex] {y}^{2} = {x}^{} \times x[/tex]

[tex] {y}^{2} = {x}^{2} [/tex]

[tex]y = x[/tex]

I hope it helps ~


Related Questions

what is (x+4) (2x-1) in standard form

Answers

Answer:

[tex]2x^{2} +7-4[/tex]

Step-by-step explanation:

Distribute x+4 into 2x-1 to get

[tex]2x^{2} +7-4[/tex]

Answer:

y= 2x^2+7x-4

Step-by-step explanation:

if you make a box plot it is easier to figure answers like this out.

Which expression is equivalent to
8
p

3
n
+
4
q

9
m

Answers

Answer:

4p-n+2q-3m

Step-by-step explanation:

:)

Satchmo bought half pound of mangoes for $6 how much would he pay for 13/4 pounds of mangoes ?

Answers

Answer: 39

Step-by-step explanation: 1/2   = 6

                                             13/4 = x

cross mutiply13/4 * 6=19.5divide both sides by 1/2answer is 39

If Satchmo bought half pound of mangoes for $6 then he pay $39 for 13/4 pounds of mangoes.

What is Ratio?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that Satchmo bought half pound of mangoes for $6

We need to find the amount he has to pay for 13/4 pounds of mangoes.

Let x be the  amount he has to pay for 13/4 pounds of mangoes..

We find the value of x by forming a proportional equation by given data.

1/2/6=13/4/x

1/12=13/4x

Apply cross multiplication

4x/12=13

x/3=13

x=39

Hence, Satchmo pay $39 for  13/4 pounds of mangoes.

To learn more on Ratios click:

https://brainly.com/question/13419413

#SPJ2

Two positive improper fractions are multiplied. Is the product sometimes, always, or never less than 1? Explain.

Answers

Answer:

The answer is yes, when two improper fractions is multiplied, the product will always be more than one.

Because when you convert an Improper fraction, the decimal value of it is always more than 1. Thus any improper fraction, added or multiplied with each other the answer will always be more than 1.

Example:

5/ 2 = this is an improper fraction. To convert it into decimal divide the denominator from the numerator

=> 5 / 2

=> 2 1/2

Drag the numbers so their absolute values are ordered from least to greatest.

Answers

Answer:

I really don't know sorry

What is the fully factored form of 32a3 + 12a2?

4a2(8a + 3)
4a(8a2 + 3a)
12a2(3a + 1)
12a(3a2 + a)

Answers

Answer:

The answer is the first one. 4a²(8a+3) Hoped that helped! :)

Varia is studying abroad in Europe. She is required to pay $3,500 (in US dollars) per year to the university; however, she must pay in euros. How many euros can Varia expect to pay per month to the university? (Round to the nearest whole euro.)

0.7306euros = 1 US dollar



213 euros
2,557 euros
30,685 euros
57,487 euros

Answers

Answer:

2,557 euros

Step-by-step explanation:

3500*0.7306=2557.1

Answer

B. 2,557 euros

Step-by-step explanation:

The population of a nearby town dropped from 7,500 to 6,000 in one year.

What was the percent decrease in the town's population that year?

Answers

Answer:

The answer is 20 percent.

The cost of a car rental is $40 plus $0.18 per mile. You are on a budget of $67. Write and solve an inequality to find the greatest distance you can drive while staying within your budget.

Answers

Answer:

You can pay a maximum of $84.

formula is:

84 = 40 + .22*m

subtract 40 from both sides of this equation to get:

44 = .22*m

divide both sides of this equation by .22 to get:

44/.22 = m

simplify to get:

m = 200

you can go at most 2

Please help asap. I really need this!!

Answers

Answer:

65

Step-by-step explanation:

istg whoever made savvas realize i need to have a converstaion with rihgt now i hate it so mcuh

Answers

Answer:

Hey :D

Step-by-step explanation:

I WILL GIVE BRAINLIEST

Answers

Answer:

I think this one will be D.  

TR=UR

Hope this helps :)

1. What is the horizontal and vertical shift for the quadratic function given by f(x) = (x+2) ^2 -4?

Answers

The horizontal shift is 2 to the left (-2) and the vertical shift is down 4 (-4)

-3 x 5 x -2y
Help please ✋

Answers

Answer:

-3 to 6 powder -2..... good luck

Please help I need the answer

Answers

Step-by-step explanation:

(i) Here in ∆ AED and ∆ CEB ,

ang . DAE = ang. BCE AD = BC ang. AED = ang. BEC

Hence by AAS congruence congruence condition ,

∆AED [tex]\cong [/tex] ∆CEB

Also ,

AE = CE . . . . . (i) BE = DE . . . . . (ii)

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

(ii) In ∆ AEB and ∆CED ,

AE = CE BE = DE ang. DEC = ang. AEB ( vertically opposite angles)

Hence by SAS condition ,

∆AEB [tex]\cong [/tex] ∆CED

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

(iii) Here ,

ang BAC = ang. DCA

Since these two angles are alternate interior Angles and equal . Hence the lines will be parallel . Also since ∆AEB is congruent to ∆CED , the corresponding sides will be equal . Hence AB = CD .

Hence Proved !

Please help me please!! −
2 -2/5x -9 < 9/10 Plsss help!
5
x

9
<
9
10

Answers

Answer:

Step-by-step explanation:

30 pts pleeeaase answer correctly

Answers

Answer:

what is the question?

Step-by-step explanation:

A recipe has a ratio of 1/3 cup of sugar to 4 cups of water if 2 cups of sugar are used how many cups of water are needed

Answers

Answer:

24 cups is the answer!

Step-by-step explanation:

Hope this helps :)

Answer:

24 cups

Step-by-step explanation:

1/3

2=6/3

4*6= 24

Help please please with this and another

Answers

Answer:

6-8k

Step-by-step explanation:

2(3-4k)=2*3-2*4k=6-8k

An algebraic expression is described as 4 less than the product of 16
and the sum of hand 5. What is the value of this expression when
h = 92
Please help me

Answers

Answer:

Below in bold.

Step-by-step explanation:

The expression is:-

f(h) = 16(h + 5) - 4

When h = 92:

f(92) =  16(92 + 5) - 4

= 16 * 97 - 4

= 1552 - 4

= 1548.

Use the digits 5,4 and 8 once each to write an odd number greater than seven hundred

Answers

845 because 800 is greater than 700 and 845 is an odd number because it ends in 5 (which is an odd number).

profa lo necesito urgente

Answers

the answer is 5x But if you know what "x" is then just multiply the x first and then the addition

please help!!! thanks!!!

Answers

Answer:

C

Step-by-step explanation:

Use the quadratic formula to find the roots. Find the factors from the roots, then multiply the factors together.

The graph below represents the linear equation y = 3/5 x- 2.​

Answers

Answer:

The y-intercept is -2 and the slope is 2/3

Step-by-step explanation:

Graph the line with slope 2 passing through the point (-1, -3).

Answers

Answer:

Step-by-step explanation:

Start with the standard equation of a straight line, y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).

We know m, so:

y = 2x + b

Now find b by using the given point (-1,-3)

y = 2x + b

-3 = 2(-1) + b

b = -1

The equation is y=2x-1

What is the positive difference between 8 and 9

Answers

Answer:

8-9=-1

just absoulte value. |-1| = 1

Step-by-step explanation:

2+2/50
what is the answer?

Answers

Answer:

2.04

Step-by-step explanation:

Answer:4/50

Step-by-step explanation:

2+2 = 4

A person invests 3500 dollars in a bank. The bank pays 5% interest compounded
semi-annually. To the nearest tenth of a year, how long must the person leave the
money in the bank until it reaches 8900 dollars?
r
A = P(1 + )nt
n

Answers

Answer: 18.9

A=8900

P= 3500

r = 0.05

n = 2 (semi-annually)

T= 18.9

will give brainliest

Answers

Answer:

D. 1356.5 cm³

Step-by-step explanation:

The volume of a cone can be represented by:

V = (π)(r²)(h/3)

Substitute the known values:

π = 3.14

r = 12

h = 9

V = (3.14)(12²)(9/3)

Square 12.

V = (3.14)(144)(9/3)

Divide 9 by 3.

V = (3.14)(144)(3)

Multiply 3.14 and 144.

V = (452.16)(3)

Multiply 452.16 and 3.

V = 1356.48

Round to the nearest tenth.

V = 1356.5.

Which fraction is equal to 0.54--

Answers

Answer:

27/50

Step-by-step explanation:

Answer:

27/50

Step-by-step explanation:

54 is another way of writing 54 hundredths, or as a fraction, 54/100. Asking for a simplified fraction is asking you to reduce the numerator and denominator by any common terms. 54 and 100 are both divisible by 2, so we get to 27/50. These have no factors in common, so 27/50 is our simplified fraction.

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