for what value of x does 4^x=(1/8)^x+5?

Answers

Answer 1

Use main properties of powers

(a^m)^n=a^{m\cdot n};(am)n=am⋅n;

\dfrac{1}{a^n}=a^{-n}an1=a−n

to simplify given equation.

1.

4^x=(2^2)^x=2^{2x}.4x=(22)x=22x.

2.

\left(\dfrac{1}{8}\right)^{x+5}=\left(\dfrac{1}{2^3}\right)^{x+5}=(2^{-3})^{x+5}=2^{-3x-15}.(81)x+5=(231)x+5=(2−3)x+5=2−3x−15.

3. Then the equation is

2^{2x}=2^{-3x-15}.22x=2−3x−15.

The bases are the same, so equate the powers:

2x=-3x-15,

2x+3x=-15,

5x=-15,

x=-3.

Answer: for x=-3.


Related Questions

Y'ALL PLEASE HELP ME I WOULD GREATLY APPRECIATE IT!!!!!:)!!!!!!

Find the measure of angle TOS in the figure below. SHOW YOUR WORK SO I CAN SEE HOW YoU GOT IT!!!!

Answers

Step-by-step explanation:

<TOS=122° [being vertically opposite angle]

Answer:

angleTOS =122°

EXPLANATION:

[ If two straight lines intersect at point O, vertically opposite angles are equal]As vertically opposite angles are equal; Hence AngleTOS=QOR=122°

Solve inequality problem (urgent help please)

Answers

Answer:

B

Step-by-step explanation:

|3m-2|=>1

1 <= 3m-2 or 3m-2 <= -1

3 <= 3m or 3m <= 1

1 <= m or m <= (1/3)

If you help me, you will get this cookie

Answers

Answer:

B. 7y - 15

Step-by-step explanation:

Simplifying

10y + -3(y + 5) = 0

Reorder the terms:

10y + -3(5 + y) = 0

10y + (5 * -3 + y * -3) = 0

10y + (-15 + -3y) = 0

Reorder the terms:

-15 + 10y + -3y = 0

Combine like terms: 10y + -3y = 7y

-15 + 7y = 0

Solving

-15 + 7y = 0

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '15' to each side of the equation.

-15 + 15 + 7y = 0 + 15

Combine like terms: -15 + 15 = 0

0 + 7y = 0 + 15

7y = 0 + 15

Combine like terms: 0 + 15 = 15

7y = 15

Divide each side by '7'.

y = 2.142857143

Simplifying

y = 2.142857143

Answer:

b. 7y-15

Step-by-step explanation:

First, write out the expression

1. [tex]10y-3(y+5)[/tex]

To simplify the expression distribute the -3 to the terms within the paratheses.

2. [tex]10y-3y-15[/tex]

Then, combine like terms to simplify further. Since 10y and -3y are like terms they can be subtracted

3. [tex]7y-15[/tex]

This means that B is the correct answer.

The option which is not a solution of the equation 2x + 3y = 6 is:
(A) (0, 2)
(B) (1, 1)
(C) (-3, 4)
(D) (3, 0).​

Answers

Answer:

Step-by-step explanation:

B OR TRUE

Look at photo I tested each thing, your answer to this question in option B

This year, a small business had a total revenue of $42,900 . If this is 35% less than their total revenue the previous year, what was their total revenue the previous year?

Answers

if this value 35% less than the total, we conclude that:

42,900 = 65%

1% = 660

100% = 66,000

if you want to check the value, just do 65% of 66000, which equals to 42,900

hope it helps :)

Which points are possible approximations for this system? Select two options.

Answers

Step-by-step explanation:

second: (2.2,-1.4)

third: (2.2,-1.35)

Step-by-step explanation:

hope it helps✨

HELP PLEASE !!


find the surface area of the cylinder and round it to the nearest tenth.​

Answers

Answer:

18.8

Step-by-step explanation:

Surface area=2*pi*r*(r+h)=2*pi*1*(3)=18.8

Tuto
Combine any like terms in the expression. If there are no like terms, rewrite the expression.
8r + 9pg - pg - pq

Answers

Answer:

8r+8pg-pq

Step-by-step explanation:

The subtractable pg cancels out one of the 9 pg's. So 9 pg-1 pg= 8 pg

Hope this helps!

A set of composite number less than 12.Express it in listing and set-builder methods

Answers

composite numbers less than 12={1,3,4,6,8,9,10}

find x
2 ^30 divided by 8^9= 2x

Answers

Answer:

see below

Step-by-step explanation:

2^30

-------

8^9

Rewriting

8^9

2^3 ^ 9

We know a^b^c = a^(b*c)

2^(3*9) = 2^27

2^30

-------

2^27

We know a^b / a^c = a^(b-c)

2^(30-27) = 2^3

Assuming you mean 2^x

2^3 = 2^x

x=3

If you mean 2x

2^3 = 8

8 = 2x

Divide by 2

4 =x

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{2^{30}}{8^9}=2x}[/tex]

[tex]\mathsf{2^{30}}\\\mathsf{= \bf 1,073,741,824}\\\\\mathsf{8^9}\\\mathsf{= \bf 134,217,728}[/tex]

[tex]\mathsf{\rightarrow \dfrac{1,073,741,824}{134,217,728}= 2x}\\\\\\\mathsf{\dfrac{1,073,741,824}{134,217,728}= \bf 8}\\\\\\\mathsf{\rightarrow \ 8 = 2x}\\\\\\\\\large\textsf{TURN\ the\ EQUATION\ around}\\\\\\\mathsf{\rightarrow\ 2x = 8}\\\\\\\large\textsf{DIVIDE 2 to BOTH SIDES}\\\\\\\mathsf{\dfrac{2x}{2}=\dfrac{8}{2}}\\\\\\\large\textsf{CANCEL out: }\mathsf{\dfrac{2}{2}}\large\textsf{ because it gives you 1}\\\\\\\large\textsf{KEEP: }\mathsf{\dfrac{8}{2}}\large\textsf{ because it gives you the answer of x}[/tex]

[tex]\mathsf{x = \dfrac{8}{2}}\\\\\\\mathsf{x = 8\div 2}\\\\\\\mathsf{x = \bf 4}\\\\\\\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \textsf{x = 4}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Ashish is 175 cm tall his sister Annu is 8% shorter than him what is Annu's height

pls help​

Answers

Answer:

8% out of 175 = ( 8 ÷ 100 ) × 175 = 14

175 cm - 14 = 161 cm

...............

Help me! thank you so much

Answers

Answer:

Step-by-step explanation:

[tex]\frac{sinxcos^3x-cos xsin^3x}{cos^42x-sin^42x} \\=\frac{sin x cos x(cos^2x-sin ^2 x)}{(cis^2 2x+sin^2 2x)(cos^2 2x-sin ^22x)} \\=\frac{2sin x cos x cos 2x}{2(1)(cos 4x)} \\=\frac{sin 2x cos 2x}{2 cos 4x} \\=\frac{2 sin 2x cos 2x}{4 cos 4x} \\=\frac{sin 4x}{4 cos 4x} \\=\frac{1}{4} tan 4x[/tex]

Answer ASAP please!
………

Answers

Answer:

47.746, answer choice C

Step-by-step explanation:

47.746

Can someone help me with this please !!

Answers

Step-by-step explanation:

I need help to...

I keep putting it in and no one has ever answered it and I'm struggling and getting stressed.

Find all three distinct roots for X³ =1. (two of them are complex mumber). And show that sum of all roots is zero.​

Answers

x ³ = 1

x ³ - 1 = 0

x ³ - 1³ = 0

Factorize the right side as a difference of cubes:

(x - 1) (x ² + x + 1) = 0

Then

x - 1 = 0   or   x ² + x + 1 = 0

The first equation yields x = 1 as a root.

For the other equation, rearrange and complete the square to get the other two roots,

x ² + x + 1/4 = -3/4

(x + 1/2)² = -3/4

x + 1/2 = ±√(-3/4) = ± i √3/2

x = -1/2 ± i √3/2

x = (-1 ± i √3)/2

Since complex roots occurs in conjugate pairs, taking the sum of these two roots eliminates the imaginary part:

(-1 + i √3)/2 + (-1 - i √3)/2 = (-1 - 1)/2 = -2/2 = -1

and adding to 1 indeed shows that the sum of roots is zero.

pls help, and explain. I will give brainliest

Answers

Answer:

Nicole should take 13 1/8 cups of snack mix.

Step-by-step explanation:

If a serving size is 7/8 and Nicole wants to take 15 serving sizes (15 7/8's), then we must multiply 7/8 by 15:

15 × 7/8

Write 15 over 1 (15 = 15/1) to make the calculations easier:

15/1 × 7/8

Multiply the numerators and denominators separately:

15 × 7 / 1 × 8

105 / 8

Instructions don't say you have to do this but I will convert this improper fraction into a mixed number:

105/8 = 13 1/8

The area CA) of a Parallelogram is found by using this formula A = BH What is the area when b is 7cm and h is 3cm?​

Answers

Answer:

Area of parallelogram = 21

Step-by-step explanation:

A = BH

Plug in

A = 7×3

Solve

A = 21

The answer will be 21.

Lilian is building a swimming pool in the shape of a right rectangular prism. The area of the base of the swimming pool is 72 square meters. The depth of the swimming pool is 3 meters. What is the volume of the swimming pool?

Answers

Answer:

216

Step-by-step explanation:

Volume of a rectangular prism = area of base * depth

Area of base: 72

Depth: 3

Volume = 72 * 3 = 216

Independent Practice


Which model is most appropriate for the set of points?

(–2, 5), (–1, –1), (0, –3), (1, –1), (2, 5)


A.
exponential


B.
linear


C.
quadratic

Answers

Quadratic because if you plot it on a graph it will look like a U

The population of a city is currently 45,000 and is declining at a rate of 2% each year. Give a formula for determining the total population after a period of t years.
Question 4 options:

A)

A = (45,000)e–0.02t

B)

A = 45,000 + e–0.02t

C)

A = (45,000)e0.02t

D)

A = 45,000 + e0.02t

Answers

Answer:

Step-by-step explanation:

The general form of this equation is

[tex]A=Pe^{rt}[/tex] where P is the initial population, e is Euler's number (a constant), r is the rate of decay, and t is the time in years.

Therefore, filling in:

[tex]A=45000e^{-.02t[/tex]

The ratio of Mitchell's age to Connor's age is 8:5. In thirty years, the ratio of their ages will be 6:5. How much older is Mitchell than Connor now?

Answers

Answer:

9 years older

Step-by-step explanation:

The ratio of their ages is 8 : 5 = 8x : 5x ( x is a multiplier )

In 30 years their ages will be 8x + 30 and 5x + 30 and the ratio 6 : 5 , so

[tex]\frac{8x+30}{5x+30}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )

5(8x + 30) = 6(5x + 30) ← distribute parenthesis on both sides

40x + 150 = 30x + 180 ( subtract 30x from both sides )

10x + 150 = 180 ( subtract 150 from both sides )

10x = 30 ( divide both sides by 10 )

x = 3

Then

Michell is 8x = 8 × 3 = 24 years old

Connor is 5x = 5 × 3 = 15 years old

Mitchell is 24 - 15 = 9 years older than Connor

The point slope formula (if possible) to write an equation of the line given the following information…we

Answers

The equation in point slope form is y - 6 = 2(x + 3)

This is from the general point slope template of [tex]y - y_1 = m(x - x_1)[/tex]

The m is the slope, which in this case is m = 2. The [tex](x_1,y_1)[/tex] is the point the line goes through. In this case, [tex]x_1 = -3 \text{ and } y_1 = 6[/tex]

If you were to solve that equation in bold for y, then you should get y = 2x+12 which is now in y = mx+b form, aka slope intercept form.

The following ordered pairs represent a function: {(-3, 1), (1, -2), (3, 0), (4, 5)}.

True or False

Answers

Answer:

false

Step-by-step explanation:

this is because there is no function of an unknown in this set

a man's income is rupees 12000 per month if the.If the rate of income tax ia rs2.50 per rs100,how much tax should he pay?​

Answers

Answer:

don't know

Step-by-step explanation:

Giải phương trình
2x+6=0

Answers

Answer: x = -3

[tex]2x+6=0\\\\2x=-6\\\\x=\frac{-6}{2} =-3[/tex]

Answer:

x= -3

Step-by-step explanation:

Solve the equation:

2x +6 = 0

We have isolate 'x'.

First subtract 6 from both sides

2x = 0-6

2x = -6

Divide each side by 2

x = -6/2

x = -3

if the ordered pairs (x-2,3y+1) and (y+1,x+3) are equal,find x and y
plz help me ​

Answers

x-2=y+1
x=y+3

3y+1=x+3
x=3y-2

3y-2=y+3
3y-y=5
2y=5
y=2.5

x=(2.5)+3
x=5.5

What is the quotient?
(-3)
(-3)²
O-9
1
o
1
9
100
O 9

Answers

Answer:

(-3)

Step-by-step explanation:

follow me if you want

Determine the sum of the first 33 terms of the following series:

−52+(−46)+(−40)+...

Answers

Answer:

1320

Step-by-step explanation:

Use the formula for sum of series, s(a) = n/2(2a + (n-1)d)

The terms increase by 6, so d is 6

a is the first term, -56

n is the terms you want to find, 33

Plug in the numbers, 33/2 (2(-56)+(32)6)

Simplify into 33(80)/2 and you get 1320

The product of two numbers is 10000.If one number is 16 times the other numbers ,find the two numbers.​

Answers

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

➯Question:

The product of two numbers is 10000. If one number is 16 times the other numbers ,find the two numbers.

Answer:

Both numbers are 25 and 400.

Step By Step Explanation:

Given that:

The product of two numbers is 10000.

One number is 16 times the other number.

To Find:

Both numbers?

Solution:

Let us consider that one number be n, in question it is stated that other number is 16 times the first number. Therefore, other number is 16n.

According to the Question :

[tex]\sf↦ Product ~of ~numbers = 10000\\\\↦ n × 16n = 10000\\\\↦ 16n² = 10000\\\\↦ n² = \sf \dfrac{10000}{16}\\\\↦ \sf n = \sqrt{\dfrac{10000}{16}}\\\\↦ \sf n = \sqrt{\dfrac{100\:\times\:100}{4\:\times\:4}}\\\\↦ \sf n = {\cancel{\dfrac{100}{4}}}\\\\➦\pmb{\underline{\boxed{\sf{\pink{n = 25}}}}}[/tex]

Hence,

1st number = n = 25

2nd number = 16n = 16 × 25 = 400

∴ Hence, both numbers are 25 and 400.

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

Answer:

(25, 400) or (-25, - 400)

Step-by-step explanation:

Let the numbers be x and y.

We have:

y = 16xxy = 10000

Substitute y and solve for x:

x(16x) = 1000016x² = 10000x² = 10000/16x² = 625x = √625x = ± 25

Then y is:

y = ± 25*16 = ± 400

The numbers are:

25 and 400 or -25 and - 400

Between which two numbers does 46 lie?
A.
between 8 and 9
B.
between 6 and 7
C.
between 5 and 6
D.
between 7 and 8

Answers

Answer:

So the sqrt(46) is between 6 and 7

Step-by-step explanation:

sqrt(46)

5*5 = 25

6*6=36

7*7=49

So the sqrt(46) is between 6 and 7

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