What is the solution set to this equation? Log2(x - 2) + log2x = 3

Answers

Answer 1

the solution set is answer A.

Answer 2

The required, solution set to the given equation is {4}. Option A is correct.

What are logarithmic functions?

A logarithmic function is a mathematical function that represents the logarithm of a number with respect to a given base. In other words, it is a function that relates a number to its logarithm. The general form of a logarithmic function is f(x) = logₐ(x).

Using the product rule of logarithms, we can combine the two logarithms on the left-hand side of the equation:

log2(x - 2) + log2x = log2[(x - 2) * x] = log2(x² - 2x)

So the given equation becomes:

log2(x² - 2x) = 3

2³ = x² - 2x

8 = x² - 2x

x² - 2x - 8 = 0

Factor this quadratic equation as:

(x - 4)(x + 2) = 0

x - 4 = 0, which gives x = 4

x + 2 = 0, which gives x = -2

However, the logarithm function is only defined for positive values of x, so the only possible solution is:

x = 4

Therefore, the solution set to the given equation is {4}.

Learn more about logarithmic function here:

https://brainly.com/question/30284289

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Related Questions

Which of the following coordinates exists on the line y = 2x + 4?
A. (2, 4)
B. (1, 5)
C. (-3, -2)
D. (-1, 3)

Answers

B and possibly Ayxjdjfhjdbvuchd

I graphed it, C (-3,-2) is correct.

[tex]8 \times {2}^{n + 2} = 32[/tex]
What is the value of n

Answers

Step-by-step explanation:

2³×2^n+2=32

2^3+n+2=2⁵

n+5=5

n=0

[tex]_____________________________________[/tex]

[tex]\sf\huge\underline\red{ANSWER:}[/tex]

[tex]\tt n = 0[/tex]

[tex]\sf\huge\underline\red{SOLUTION:}[/tex]

[tex]\tt8 \times {2}^{n + 2} = 32 \\ = \tt {2}^{3} \times {2}^{n + 2} = 32 \\ = \tt {2}^{n + 5} = 32 \\ = \tt {2}^{n + 5} = {2}^{5} \\ = \tt n + 5 = 5 \\ = \tt n = 5 - 5 \\ = \large\boxed{\tt{\green{n = 0}}}[/tex]

[tex]_____________________________________[/tex]

[tex]\large\boxed{\sf{\green{CarryOnLearning}}}[/tex]

[tex]\large\boxed{\sf{\red{MathDemonQueenシ︎✌︎}}}[/tex]

[tex]\large\boxed{\sf{\green{ItsMoreFunInThePhilippines✌︎}}}[/tex]

#1
You and your family need to take a taxi to get around town on
your vacation. The taxi service charges $7.50 for the initial
pickup of you and your family and $0.25 per mile. Write an
equation to represent this situation. Then, calculate how much
it would cost if you took the taxi for a 12 mile trip.
Equations
Solutions
y = 0.25x + 7.75
А A
$10.50
3
y = 7.50x + 0.25
B
$18.00
y = 0.25x + 7.50
$90.25
5

Answers

The requested equation is

C(m) = 7.50 + 0.25*m,

where C(m) is the total cost (in dollars) for "m" miles.

Make the plot on your own.

Answer:

Equation: y = 0.25x + 7.50

Cost: $10.50

Step-by-step explanation:

Let x be the number of miles and y be the total cost in $.

y = 0.25x + 7.50

If we want to find the total cost of a 12 mi trip, we plug in x=12.

y = 0.25 * 12 + 7.50

y = 3 + 7.50

y=10.50

Find the volume of this cone.
Round to the nearest tenth.
10ft
6ft

Answers

Answer:

301.6 ft³

Step-by-step explanation:

Volume of the cone = ⅓*πr²h

Where,

radius (r) = 6 ft

height (h) = √(10² - 6²) => Pythagorean theorem

h = √(100 - 36)

h = √64

h = 8 ft

Plug in the values

Volume = ⅓*π*6²*8

Volume = 301.6 ft³ (nearest tenth)

2 divided by 0.75 please help

Answers

Answer:

8/3

Step-by-step explanation:

2/ (3/4) = 2*4/3 =8/3

Answer-
2/.75= 2.6667

find the 11th term of the series
8,14,20,26.......

Answers

Answer:

a11 = 8+(11-1)6

a11 = 8+54

a11=68

hopefully this is correct

Step-by-step explanation:

HURRYY!!!
which exponential function is represented by the graph

Answers

Answer:

Apr 16, 2018 — p>Which exponential function is represented by the graph?f(x) = 2(1/2)^x f(x) = 1/2(2)^x f(x) = 1/2

Step-by-step explanation:

giải phương trình y′′ − 7y′ + 6y = sin x.

Answers

Start with the underlying homogeneous equation:

[tex]y''-7y'+6y=0[/tex]

which has characteristic equation

[tex]r^2-7r+6=(r-6)(r-1)=0[/tex]

with roots at r = 6 and r = 1. So the characteristic solution is

[tex]y_c=C_1e^{6x}+C_2e^x[/tex]

Now for the particular solution, we can use the method of undetermined coefficients, with the following ansatz (the "guess" solution) and its derivatives,

[tex]y_p=a\cos x+b\sin x[/tex]

[tex]{y_p}'=-a\sin x+b\cos x[/tex]

[tex]{y_p}''=-a\cos x-b\sin x[/tex]

Substituting these into the original equation gives

[tex](-a\cos x-b\sin x)-7(-a\sin x+b\cos x)+6(a\cos x+b\sin x)=\sin x[/tex]

[tex](5a-7b)\cos x+(7a+5b)\sin x=\sin x[/tex]

[tex]\implies\begin{cases}5a-7b=0\\7a+5b=1\end{cases}\implies a=\dfrac7{74},b=\dfrac5{74}[/tex]

So the particular solution is

[tex]y_p=\dfrac7{74}\cos x+\dfrac5{74}\sin x[/tex]

and hence the general solution is

[tex]y=y_c+y+p=\boxed{C_1e^{6x}+C_2e^x+\dfrac7{74}\cos x+\dfrac5{74}\sin x}[/tex]

Help with this please

Answers

Answer:

I would say 4 to 6 since everything else is decreasing

[tex]4x -6x- 5 - 8\\-2x- 13[/tex]

I hope this helps!

Answer:

- 2 - 13

Step-by-step explanation:

( 4 x - 5 ) - ( 6 x + 8 )

= 4 x - 5 - 6 x + 8

Arranging like terms together

= 4 x - 6 x - 5 - 8

= - 2 x - 13

Center(1/2+1/3) Radius=2/3

Answers

Answer:

[tex]{ \bf{ {x}^{2} + {y}^{2} - \frac{1}{2} x - \frac{1}{3} y}} - \frac{1}{12} = 0[/tex]

How much would you pay for: 240 textbooks at $15.40 each, 100 pens at $1.25 each and 30
dozen erasers at 95c each?

Answers

Answer:

384950c or $3849.50

Step-by-step explanation:

240x1540=369600

100x125=12500

30x95=2850

369600+12500+2850=384950

graph the function.
for the function whose graph is shown below, which is the correct formula for the function?

A. y = -x + 1
B. y = x - 1
C. y = -x - 1
D. y = x + 1

Answers

Answer:

y =x+1

Step-by-step explanation:

The y intercept is 1

The slope is positive

We go up 1 and to the right 1

y = mx+b where m is the slope and b is the y intercept

y = 1x+1

y =x+1

Steven earns extra money babysitting. He charges $40.50 for 6 hours and $54.00 for 8 hours. Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he charges.

Answers

Answer:

6.75 * x =y

Step-by-step explanation:

In this question, for is a keyword here we can use to represent division. If he charges $40.50 for 6 hours, this means we can represent this as [tex]\frac{40.50dollars}{6 hours}[/tex] to calculate the amount babysitting costs for an hour. Our answer is then [tex]\frac{6.75 dollars}{1 hour}[/tex]. A similar division of $54.00 for 8 hours results in a calculation of [tex]\frac{54.00 dollars}{8 hours} = \frac{6.75 dollars}{1hour}[/tex]. This means that for each hour, he charges 6.75 dollars, the same amount of money each hour.

Given this information, we can say that an equation to represent this relationship would be that, to calculate the total money Steven earns, we can multiply 6.75 dollars by the amount of hours he works, as he earns 6.75 dollars for each hour, making our equation 6.75 * x =y, with y representing the total amount he charges. If your teacher would

parabola
Given that tanθ= [tex]-\frac{9}{4}[/tex] and [tex]\frac{\pi }{2\\}[/tex]<θ<π , find the exact values of the trigonometric functions.

Answers

9514 1404 393

Answer:

sin(θ) = (9√97)/97cos(θ) = (-4√97)/97csc(θ) = (√97)/9sec(θ) = (-√97)/4cot(θ) = -4/9

Step-by-step explanation:

The angle is in the 2nd quadrant, where the sine is positive and the cosine is negative.

tan^2(θ) +1 = sec^2(θ) = (-9/4)^2 +1 = 97/16 ⇒ sec = -(1/4)√97

cot(θ) = 1/tan(θ) = -4/9

csc^2(θ) = cot^2(θ) +1 = (-4/9)^2 +1 = 97/81 ⇒ csc = (1/9)√97

sin(θ) = 1/csc(θ) = (9√97)/97

cos(θ) = 1/sec(θ) = (-4√97)/97

If 137 is subtracted from three times of square of a natural number the result is 55. Find the number

Answers

Answer:

Step-by-step explanation:

Let the unknown number be x.

Therefore, we can write the question as a mathematical statement and this will be:

3x^2 - 137 = 55. (Note: ^2 = to the power of 2 or "squared"

(In the question, we can break it up as being three times of a square of a natural number = (3x^2) and 137 is subtracted from = (- 137) and the result is 55 = (= 55). Therefore, this gives 3x^2 - 137 = 55

Then, we add 137 first to get rid of the (-137)

Therefore:

3x^2 = 192

Then, we divide 3 from both sides to get rid of the (3) in (3x^2).

Therefore,

x^2 = 64.

So, we square root 64. This gives

x = 8.

Therefore, the answer is 8.

How many sticks would be in pattern number n

Answers

Answer:

hey. pls post a pic of the pattern or type in the number of sticks in each term so we could help tou determine the nth term

what is the mode for the data set
x
x x x
x x x x x x
_______ __
5 6 7 8 9 10 options 7.8
5
8
9

Answers

Answer:

Step-by-step explanation:

The mode of a data set is the number that appears most

Find the x- and y intercepts in the table write your answers as separate coordinates

Answers

Answer:

1: x intercept:2 y intercept:5

2: x intercept:-7 y intercept:1

3: x intercept:2 y intercept:-2

4: x intercept: 1 y intercept: -2

Step-by-step explanation:

The y intercept is whenever the x unit is at 0, and the x intercept is whenever the y intercept is at 0.

$5200 = 0.84p

p = $5200/0.84 = $6190.48

The price before the discount was $6190.48.

For an outdoor concert by the city orchestra, concert organizers estimate that 19,000 people will attend if it is not raining. If it is raining, concert organizers estimate that 4000 people will
attend. On the day of the concert, meteorologists predict a 60% chance of rain. Determine the expected number of people who will attend this concert.
It is expected that people will attend the concert.

Answers

Answer:

Hope it helps you stay safe<3

Miguel borrowed $1,800 for 2 years and ended up paying $180 in simple interest what was the interest rate

Answers

Answer: 103.534%

I used a calculator and everything

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