If 64^x=1/256^y then the value of 3x+4y is​

Answers

Answer 1

Given,

[tex]\longrightarrow\rm{64^x=\dfrac{1}{256^y}}[/tex]

We have to find out the value of 3x + 4y.

Multiplying both sides by [tex]\rm{256^y}[/tex] we get,

[tex]\longrightarrow\rm{64^x\cdot256^y=1}[/tex]

Then we will write 64 and 256 as powers of 4 as,

[tex]\rm{64=4^3}[/tex]

[tex]256=4^4[/tex]

Then,

[tex]\longrightarrow\rm{(4^3)^x\cdot(4^4)^y=1}[/tex]

[tex]\longrightarrow\rm{4^{3x}\cdot4^{4y}=1\quad\quad[\because(a^m)^n=a^{mn}]}[/tex]

[tex]\longrightarrow\rm{4^{3x+4y}=1\quad\quad[\because a^m\cdot a^n=a^{m+n}]}[/tex]

Now we will take log to the base 4.

[tex]\longrightarrow\rm{\log_4(4^{3x+4y})=\log_4(1)}[/tex]

[tex]\small\text{$\longrightarrow\rm{(3x+4y)\log_4(4)=\log_4(1)\quad\quad[\because\log_b(a^m)=m\cdot\log_b(a)]}$}[/tex]

We have,

[tex]\rm{\log_4(4)=1}[/tex]

[tex]\log_4(1)=0[/tex]

Then,

[tex]\longrightarrow\rm{(3x+4y)(1)=0}[/tex]

[tex]\longrightarrow\rm{\underline{\underline{3x+4y=0}}}[/tex]

Hence 0 is the answer.


Related Questions

Help me please m, it due soon

Answers

Surface area= 2(6x15)+2(7x15)+2(6x7)
=180+210+84
=474m

Volume=15x6x7
=630m^2

Jackson will buy the items listed below. He has $422.76 in his checking account. He had a stored-valued card worth $75. He withdrew cash to cover the remaining cost of the items. His bank automatically deducts a fee of $2.50 from the account for the withdrawal. After purchasing the items, how much money is left in Jackson's account?

Items. Cost($)

video game. 44.99

video game console. 299.49

a
$150.78
b
$269.48
c
$344.48
d
$497.76

Answers

Answer:

A

Step-by-step explanation:

44.99+299.49 = $344.38

$344.38 - store card ($75) = $269.48

422.76 - 269.48 - 2.5 = $150.78

Therefore answer is A

Ruth buys 19 identical tickets for £280.25.
Estimate the cost of one ticket.

Answers

Answer:

The cost of one ticket is $14.75

Step-by-step explanation:

To find the cost of one ticket we need to divide 280.25 by 19

=$14.75

plz mark me as brainliest

Answer:

The cost of one ticket is $14.75

Step-by-step explanation:

The cost of one ticket is $14.75

To find the cost of one ticket we need to divide 280.25 by 19

=$14.75

please mark as brainliest

Please I’m struggling

Answers

Answer:

120 cm³

Step-by-step explanation:

multiply all the numbers together

4*6*5

120

120 cm

have a nice day bye

Can someone help me please?

Answers

I think the mean is 15

Answer and explanation

Answers

Answer:

200in

Step-by-step explanation:

theres two squares in this face, so find the area of them

A = 10x10

A = 100in

A = 10x10

A = 100in

100 + 100 = 200in

Plz help fill in the blanks the options are

108 sq ft
21 sq fr
22 sq ft

Answers

Answer:

12

9

21

Step-by-step explanation:

The top rectangle is L*W

L = 6

W = 2

Area = 6 * 2 square Feet

Area = 12 sq ft.

The Bottom figure is a square

Area = s * s

s = 3 feet

Area = 3 * 3 = 9 square feet

Total

12 + 9 = 21 square feet.

PLEASE HELP ME ON THIS QUESTION ASAP!!!! NO LINKS

Answers

Answer:

4π in.

Step-by-step explanation:

formula circumference= 2πr

r = half of diameter

Given the sequence {-2,5,12,19...} ,find a34

Answers

Answer:

the answer is in the attachment

The 34th term of the arithmetic value progression is a₃₄ = 229

What is Arithmetic Progression?

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the sequence be represented as A

Now , the value of A is

A = {-2,5,12,19...}

And , to find the 34th term of the sequence {-2, 5, 12, 19, ...}, we first need to find the common difference between consecutive terms:

The common difference = 5 - (-2) = 7

So, to get the 34th term, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n-1)d

where a1 is the first term, d is the common difference, and n is the term number we want to find.

Plugging in the values we have:

a₃₄ = -2 + (34-1)7

a₃₄ = -2 + 231

a₃₄ = 229

Hence , the 34th term of the sequence is 229

To learn more about arithmetic progression click :

https://brainly.com/question/1522572

#SPJ3

Write a numerical expression Add 8 and 7 and then multiply by 2 ? Guys i need help ASAP please write a numerical expression HELP ME brainlest

Answers

Answer:

30

Explanation

Add 8 and 7. 8 + 7 = 15. 15 x 2 is 30

Answer:

the answer will be 30

Step-by-step explanation:

Add 8 and 7. 8 + 7 = 15. 15 x 2 is 30

you throw a basketball from a height of 4 feet with an upward velocity of 15 feet per second the function h=-16t^2+15t+4 gives the height of the basketball after t seconds when does the basket ball hit the floor round your answer to the nearest tenth

Answers

Answer:

After 1.2 seconds

Please don’t not provide links I just need steps to understand

What is measure of egd

Answers

Answer:

I got you fam.

the answer is 180

Step-by-step explanation:

so if you look at how HE is 115 then you take 180 and -115 to get 65 so your answer is 65.

Hoped that helped! :)

PLEASE HELP ASAP HELPPPPP PLEASEEE!!!! find the value of x. round to the nearest tenth
x
12
4
x =?

Answers

Answer:

70.5

Step-by-step explanation:

cos x = [tex]\frac{4}{12}[/tex]

x = [tex]cos^{-1}\frac{1}{3}[/tex]

x = 70.53

The price of BZG CO's stock is tracked over several days, as displayed in the table below. Based on the data given, what linear equation can be used to predict the price of this stock in the future? Round the variables to 3 decimal places.

Answers

Answer:

Y= 1.165x18.703

And the equation from the previous problem to predict the price BZG stock on day 30 is y=1.165(30) + 18.703 -$53.65

A muffin recipe calls for 1 cup of flour, 1/2 cup of sugar and 3/4 cup of milk and makes 20 muffins. How much of each ingredient would you need to make 120 muffins?

Answers

Answer:

well you multiple 20 by 6 to get 120, so that means multiple everything by 6

SO, 6 cups of flour, 3 cups of sugar, and 4 1/2 cups of milk

Find the value of x.
(3x+20) º
12°

Answers

Answer:

x=32°

Step-by-step explanation:

2x+3x+20=180 co interior angle

5x=180-20

x=160/5=32°

Answer:

12°

Step-by-step explanation:

a straight line adds up to 180°

(3x+20)+2x=180

3x+2x+20=180

5x+20=180

5x=180-20

5x=60

5x/5=60/5

x=12

x=12°

Find the distance between the pair of points (-6.-17) and (-8.-19) The distance is (Round to the nearest thousandth as needed.)​

Answers

Answer:

2.83

Step-by-step explanation:

d= Square root of (x2 - x1 )^2 +( y2- y1)^2

from the point given you

x1= -6

y1 = -17

x2 = -8

y2 = -19

by applying the formula

Square root of ( -8 - (-6))^2 + ( -19 - (-17))^2

Square root of (-8+6) + (-19+17)^2

Solve for x. With explanation

Answers

Answer:

129

Step-by-step explanation:

the sum of the interior angles of a quadrilateral is 360, so you add 71+112+48 and subtract it from 360 to get x

Which equations are correct? Select each correct answer.
6a5(6a5)=36a25
6b4(−3b4)=−18b8
5x4(4x2)=20x6
3z7(4z2)=12z9

Answers

Answer:  

2, 3, 4,

Step-by-step explanation:

I took the k12 quiz and i remeber putting these as my answer.

Hope this helps!

Solve for all values of x by factoring.

x^2+10x+12=2x+5

Answers

Answer:

x = -1, -7

Step-by-step explanation:

=> x² + 8x + 7 = 0

=> (x + 1) (x + 7) = 0

=> x = -1, -7

The first step is to distribute the 2x+5 so then you get x^2+8x+7 and then you can solve and get
x=-7
x=-1

Fill in the blank. The solution to 2 x - 2 + 5 = 13 is ______

Answers

2x = 13 - 5 + 2
2x = 10
x = 5

Help please not sure what it can be!

Answers

Answer:

y=40x-30

Step-by-step explanation:

How many tiles will figure 13 have ??
FREE POINTS!

Answers

Answer:

more tiles than i laid in ur momms

Step-by-step explanation:

Figure 13 has 11 tiles

Find the Are of the Shaded Region

Answers

Area of 3/4 circle = 3/4 x π x r²
= 3/4 x 22/7 x 6²
= 84.86cm²

That should be the correct answer
Hope this helps!!

Answer:

≈ 84.8 cm²

Step-by-step explanation:

The area of the shaded region is calculated as

area of circle - area of unshaded sector

area of circle = πr² = π × 6² = 36π

unshaded area = area of circle × fraction of circle

                          = 36π × [tex]\frac{90}{360}[/tex] = 36π × [tex]\frac{1}{4}[/tex] = 9π

area of shaded region = 36π - 9π = 27π ≈ 84.8 cm² ( nearest tenth )

Jed wants to earn 25% annual net income on his $50,000 cash investment in property his annual expense of owning the property are $9600 what monthly rent must jed charge

Answers

Answer: $1,842

Step-by-step explanation:

John wants to earn 25% of his investment of $50,000 which is:

= 25% * 50,000

= $12,500

He has expenses of $9,600 yearly so the rent he should charge per year in order to make his 25% requirement as income is:

= Expenses + Return

= 9,600 + 12,500

= $22,100

Rent per month is:

= 22,100 / 12

= $1,842

if there are 24 boys and 6 girls in a room, fill out all of the possible ratios of boys to girls that could be made.

Answers

Answer:

4:1, 6:2, 12:3, 24:6

Step-by-step explanation:

24 boy

6 girls

possible ratio

24 ÷ 6 = 4

6÷ 6 = 1

4 : 1

24 ÷ 3 = 6

6 ÷ 3 = 2

6 : 2

24 ÷ 2 = 12

6 ÷ 2 = 3

12 : 3

24 ÷ 1 = 24

6 ÷ 1 = 6

24 :6

The dot plot below shows the drawing scores of some students: A number line is shown from 1 to 5 in increments of 1. The horizontal axis label is Score. There is 1 dot above 1, 2 dots above 2, 3 dots above 3, 4 dots above 4, and 5 dots above 5. The title of the line plot is Dance Scores. Which statement best describes the shape of the data? It is not symmetric and has a peak at 1. It is not symmetric and has a peak at 5. It is symmetric and has a peak at 1. It is symmetric and has a peak at 5.

Answers

Answer:

10 maybe

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Plzzz help me!!! ASAP

Answers

The answer is 7 and 8

Which expression is equivalent to (r^-7)^6?
A: r^42
B: 1/r^42
C: -7r^6
D: 1/r​

Answers

Answer:

B

Step-by-step explanation:

(r^-7)^6 = r^-42 = 1/r^42

Help im sister needs help and i can't help her im doing my school work !

Answers

answer is 73 because blah blah blah blah
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