Answers
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:
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Related Questions
#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
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
HURRYY!!!
which exponential function is represented by the graph
Answers
Answer:
Apr 16, 2018 — p>Which exponential function is represented by the graph?</p><span>f(x) = 2(1/2)^x </span><span>f(x) = 1/2(2)^x </span><span>f(x) = 1/2
Step-by-step explanation:
[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]
2 divided by 0.75 please help
Answers
Answer:
8/3
Step-by-step explanation:
2/ (3/4) = 2*4/3 =8/3
2/.75= 2.6667
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.
(-5/2;5) (1/7;1) (1;-2) (2;-2)
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
Evaluate ∬_D▒〖42y^2-12x dA〗 where D={(x,y) 0≤x≤4 ,(x-2)2 ≤y≤6
Answers
Resuelve el siguiente problema aplicado al sistema de ecuaciones, utilizando cualquiera de los tres métodos aprendidos: Sergio tiene $ 1.950 en monedas de $ 100 y de $ 50. En total tiene 24 monedas. Determina cuántas monedas son de $ 100 y cuántas de $ 50.
Answers
Answer:
Tiene 9 monedas de $50 y 15 monedas de $100.
Step-by-step explanation:
Sergio tiene $1950 en monedas de $100 y $50, entonces la primera ecuación es la siguiente:
[tex] 100x + 50y = 1950 [/tex] (1)
Ahora, en total tiene 24 monedas:
[tex] x + y = 24 [/tex] (2)
De la ecuación (2) tenemos:
[tex] x = 24 - y [/tex] (3)
Ahora introduciendo la ecuación (3) en la ecuación (1) y resolviendo para "y" nos queda:
[tex] 100(24 - y) + 50 y = 1950 [/tex]
[tex] 2400 - 100y + 50y = 1950 [/tex]
[tex] y = \frac{450}{50} = 9 [/tex]
Con la ecuación (3) podemos hallar el valor de "x":
[tex] x = 24 - 9 = 15 [/tex]
Por lo tanto, tiene 9 monedas de $50 y 15 monedas de $100.
Espero que te sea de utilidad!
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:
5
Step-by-step explanation:
The mode of a data set is the number that appears most
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)
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) = -4/9Step-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:
8
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.
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]
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
What's the area of the green face?
Answers
Answer:
242
Step-by-step explanation:
14 * 7 = 98
18 * 8 = 144
98 +144 = 242
x +4
5) 4
4
please help!
Answers
What does X equal ????
Answers
cos(X) = (20^2 + 18^2 - 22^2) / (2 x 20 x 18) = 0.33333...
X = cos^-1(0.3333...) = 70.5 degrees (1 dp)
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]
A store decreases the price of a sofa by 16% this month only, to $5200. What was the price before the
discount
Answers
9514 1404 393
Answer:
$6190.48
Step-by-step explanation:
The price is now 1 -16% = 84% of the original price (p).
$5200 = 0.84p
p = $5200/0.84 = $6190.48
The price before the discount was $6190.48.
Find a counter example for each of the following conditional statements. There are multiple correct answers. This question will be graded manually.
If a number ends in five, then it will divide evenly by two.
Answers
9514 1404 393
Answer:
5
Step-by-step explanation:
The number 5 is a counterexample, as is any number ending in 5.
5 ÷ 2 = 2 remainder 1
The non-zero remainder indicates 5 is not divisible evenly by two.
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<3Help with this please
Answers
Answer:
I would say 4 to 6 since everything else is decreasing
Step-by-step explanation:
PLS HELP ME ILL GIVE BRAINLIEST FOR THE 2 QUESTIONSSS
Answers
Answer:
can you turn up your brightness i can barely see it
Step-by-step explanation:
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
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
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
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:
6) Find the difference of (4x - 5) and (6x + 8)
Answers
Answer:
[tex]-2x- 13[/tex]
Step-by-step explanation:
Hi there!
[tex](4x - 5)-(6x + 8)[/tex]
Open up the parentheses
[tex]4x - 5-6x - 8[/tex]
Combine like terms
[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
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
238/35 mixed number simpified
Answers
Answer:
6 4/5
Step-by-step explanation:
Find the Greatest Common Factor (GCF) of 238 and 35, if it exists, and reduce our fraction by dividing both numerator and denominator by it. GCF = 7,
=238÷7/35÷7=34/5
Converting to a mixed number using long division with remainders for 34 ÷ 5.
34÷5=6R4
Therefore:
34/5=6 4/5