The solution involves converting the equation into exponential form, simplifying the expression, and solving for x. The final solution is x = 7/4.
1. Let's solve the equation step by step. First, we can use the property of logarithms that states log(a) + log(b) = log(ab) to rewrite the equation as log(x^2) = log(2) log(4x - 6). Applying another logarithmic property, we can rewrite this as log(x^2) = log((4x - 6)^log(2)). Since the logarithm of a number to the base of the same number cancels out, we have x^2 = (4x - 6)^log(2).
2. To simplify further, we can convert the equation into exponential form. Taking both sides to the power of 10, we get 10^(x^2) = 10^((4x - 6)^log(2)). Now, we can equate the exponents, resulting in x^2 = (4x - 6)^log(2) = 2^log(2)^(4x - 6) = 2^(2(4x - 6)) = 2^(8x - 12).
3. Next, we can equate the bases of the exponential expression, which gives x^2 = 2^(8x - 12). To solve for x, we can take the logarithm of both sides using the base 2 logarithm. This gives log2(x^2) = log2(2^(8x - 12)), which simplifies to 2 log2(x) = 8x - 12.
4. By substituting u = log2(x), the equation becomes 2u = 8x - 12. Rearranging the terms, we have 8x = 2u + 12. Dividing both sides by 8, we get x = (2u + 12)/8. Substituting back u = log2(x), we obtain x = (2 log2(x) + 12)/8.
5. Simplifying further, we have x = (log2(x) + 6)/4. Multiplying through by 4, we get 4x = log2(x) + 6. Rearranging the terms, we have log2(x) - 4x = -6. At this point, we can solve the equation numerically using numerical methods or graphing calculators. The approximate solution is x ≈ 1.75. Therefore, the final solution to the logarithmic equation 2 log(x) = log(2) log(4x - 6) is x ≈ 1.75 (or x = 7/4).
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Find x. Simplify completely.
x = [?]
Enter the number that belongs in the green
Please helppp
Step-by-step explanation:
Answer is 20.
Please use paythagoras theorem in every triangles.
Help me please, I’m a freshman taking a tenth grade course. I’m lost :/
Answer:
what is the question? Please ask a question.
Taylor and Katy repeatedly toss a fair coin. Katy wins if heads are thrown, Taylor wins if tails are thrown, and the game ends when someone has won three times. Katy is currently behind 1 to 2. The chance Katy wins is:
Answer:
25%
Step-by-step explanation:
In order to find the chance/probability that Katy wins we need to first find the probability of her winning a single coin toss and then multiply it twice. This is because Katy has 1 win already and needs two more win the entire game. Since a coin toss only has 2 options and only 1 of those outcomes will cause Katy to win, then this means that the probability of Katy winning is 1/2 or 50%. Now we can multiply this probability twice to get the probability of Katy winning the entire game
1/2 * 1/2 = 1/4 or 25%
Help me out plz ????
96 cm^2
Each side has an area of 24 cm^2, so just multiply that by 4
20 pts help...................
Answer:
[tex]3 \frac{3}{4}[/tex]
Step-by-step explanation:
We have a right rectangular prism and the question is asking for the volume.
Look for the formula of volume :
V = LWH
L being length
W being width
H being height
The formula is basically saying to multiply all sides together, so let's do as so.
[tex]2*1\frac{1}{4} * 1\frac{1}{2}[/tex]
= [tex]3 \frac{3}{4}[/tex]
Answer:
c
Step-by-step explanation:
Sheila is flying a kite with a string that makes a 59-degree angle with
the sand. If the height of the kite above the ground is 97 feet, how
long is the string? (Please use the exact ratio to calculate the missing
side and round your answer to the nearest hundredth.)
I'm assuming we're looking for the hypotenuse?
[tex]sin = \frac{opp}{adj} [/tex]
[tex] \sin(59) = \frac{94}{hyp} [/tex]
[tex]hyp = \frac{94}{ \sin(59) } [/tex]
[tex]hyp = 109.6635393382 feet[/tex]
The string is 109.66 feet long.
Andrew estimates the attendance at the game to be 550 people. There ar
actually 621 people at the game. What is the percent error?
Answer:
~8.9%
Step-by-step explanation:
Write and equation of the line in slope intercept form that passes through the points. (0,1) (2,4)
I would need you to tell me the answers to each question (3 questions)
Step-by-step explanation:
For no. 4
x = 180° - 98° - 50°
x = 32°
For no. 5
x = 180°- 67°-56°
x = 57°
For no. 6
x = 180° - 22° - 47°
x = 111°
Hope it will help :)❤
3x-4+2x=6+2x-4
What will be the x?
Answer:
x=2
Step-by-step explanation:
To find the value of x
3x+4 = 2x+6
3x-2x = 6–4
x=2
The value of x is 2.
Platter has six veggie wraps 12 turkey wraps and cost 64.50 another platter has eight veggie wraps turkey wraps and cost 56 what is the cost of a veggie wrap
Answer:
$3.25
Step-by-step explanation:
The computation of the cost of a veggie wrap is shown below:
Let us assume the veggie strap be x
And the turkey wrap be y
Now the equations are
6x + 12y = $64.50
x + 2y = $10.75
8x + 8y = $56
x + y = 7
Now
x + 2y = $10.75
x + y = $7
y = $3.75
So x = $7 - 3.75
= $3.25
a scientist is studying wildlife. she estimates the population of bats in her state to be 270,000. she predicts the population to grow at an average annual rate of 2.9 percent
using the scientists prediction, create an equation that models the population of bats, y, after t years.
Answer:
Step-by-step explanation:
y = 270,000 ×1.029^t
Paula salió de su casa rumbo al trabajo avanzo 8km al este y 13km al norte. Si hubiera un camino recto desde su casa a su trabajo ¿Que distancia recorrería por ese camino?
Answer:
15.26km
Step-by-step explanation:
Con la informacion de la pregunta e hecho un diagrama de la situacion. Podemos ver en el diagrama que el recorido forma un triángulo rectángulo. Entonces para saber la distancia que recorreria por el camino recto desde su casa a su trabajo tendriamos que calcular el valor de x, que se puede calcular usando el teorema de pitagoras que es el siguiente.
[tex]a^{2} + b^{2} = c^{2}[/tex]
donde a y b son el ancho y el alto del triangulo y el c seria x
[tex]8^{2} + 13^{2} = x^{2}[/tex]
[tex]64 + 169 = x^{2}[/tex]
[tex]233 = x^{2}[/tex]
[tex]15.26 = x[/tex]
Finalmente, podemos ver que la distancia seria 15.26km
Juanita borrowed $600 to purchase a new computer. She was charged 7% interest for two years. She used the simple interest formula to find the interest.
I = 600(7)(2)
What error did Juanita make and how will her error affect the interest she calculates? Explain
{_____________________________
whoever does best get brainliest
Answer:
The correct formula should be I= 600(0.07)(2). Juanita made a very common error, she didn't put the percentage of interest in decimal form; or she didn't put the percent sign on it so we know to put it in decimal form. Her error will make a big difference; with using her calculations the answer would be $8,400. With the correct formula the answer is $84.
Hope this help! :)
Given :-
Juanita borrowed $600 .Rate of Interest = 7% .Time = 2yrs .To find :-
Error made by her.Answer :-
As we know that the formula for Simple interest is ,
SI = P*R*T / 100Substitute ,
I $600* 7 * 2 / 100 I = $ 84 .So here she did not write 7 % as 7/100 instead she wrote 7 .
Chloe earned a grade of 87% on her multiple choice math final that had a total of 200
problems. How many problems on the final exam did Chloe answer correctly?
200 x 0.87 = 174
She answered 174 questions correctly.
Answer:
Chloe answered 174 problems correctly.
Explanation:
To find percentage, you would multiply the percentages decimal to the total.
0.87x200=174
please please answer will give brainliest
Answer:
c
Step-by-step explanation:
.5xBxH=.5x16x5=8x5=40
Answer:
c
Step-by-step explanation:
sources: dude trust me
(-10,-8), (8, 10) what the slope for this plz
Answer:
1
Step-by-step explanation:
y2 - y1/x2 - x1
10 + 8/8 + 10 = 18/18 = 1
Factorize:36 X ^2 + 36 X + 8 / 2 x - 1 pls help me answer thisssss by tonight plsss
Answer:
36X2 + 40X − 1 = 0
Find the lowest common multiple. 4 and 22
Answer:
44
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
hope this helps
PLEASE HELP!!!! 25 POINTS!!!
don't need to answer all but someone please help with a few questions!!!
(GRAPH INCLUDED)
Which variable did you plot on the x-axis and which variable did you plot on the y-axis? Explain why you assigned the variables in that way.
Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined.
What does the slope of the line represent within the context of your graph? What does the y-intercept represent?
Test the residuals of two other points to determine how well the line of best fit models the data.
Use the line of best fit to help you to describe the data correlation.
Using the line of best fit that you found in Part Three, Question 2, approximate how tall is a person whose arms span is 66 inches?
According to your line of best fit, what is the arm span of a 74-inch-tall person?
Answer:
x variable
Step-by-step explanation:
HOPE IT WILL HELP YOU
120 pounds decreased by 5%
Answer:
114 pounds
Step-by-step explanation:
math help please (question 9)
*theres also a hint*
Answer:what are the answer choices
Step-by-step explanation:
Answer:
Point A = (0,1) Point B = (1,2) Point C = (2,4)
Step-by-step explanation:
To find a point's "ordered pair" (x and y coordinates), consider each line a single digit unless the problem states/shows otherwise (ex. if the lines were evidently counting by 2's). Here, we can see each line represents a single digit. First count how many lines to the left/right of the y axis the point is (this will be your x point - ex. point B in this problem has an x valued at 1 because the point was one line to the right of the bold vertical line in the middle (the y axis). If the point is to the left, it is a negative x value, right would be positive, and if the point is on the y axis line. x is 0. You are essentially counting how far along the x axis the point is. Same applies to the y values, given you do the opposite and count how far from the x axis (horizontal bold line) the point is. Above that line is positive, below is negative, and again, if the point is on the x axis (bold horizontal line), the y value is 0. Then simply fill your values in in their corresponding places in the brackets: (x,y).
Hope this helps :) I know math can be especially hard to grasp so it's always okay to ask for help/explanation.
16. Solve the system of equations by graphing.
y = x + 8
y = - x- 6
Answer:
Step-by-step explanation:
x + 8 = -x - 6
2x + 8 = -6
2x = -14
x = -7
y = -7 + 8
y = 1
(-7, 1)
8-3(6-6x) please help
Answer:
-10 + 18x
Step-by-step explanation:
8-3 (6-6x)
distribute -3 with the numbers inside the parenthesis and you end up with
8 -18 + 18x
and you simplify by subtracting 18 from 8 so you get
-10 + 18x
The simplified form of the expression 8 - 3(6 - 6x) is -10+18x.
To simplify the expression 8 - 3(6 - 6x), we can apply the distributive property to remove the parentheses.
Distribute the -3 to both terms inside the parentheses:
8 - 3 × 6 + 3 × 6x
Simplify the multiplication:
8 - 18 + 18x
Combine like terms:
-10 + 18x
Therefore, the simplified expression is -10 + 18x.
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Susanna's family traveled 5 7 of the distance to her grandmother's house on Saturday. They traveled 1 2 of the remaining distance on Sunday. What fraction of the total distance to her grandmother's house was traveled on Sunday?
Answer:
1/7
Step-by-step explanation:
Please write these fractions as 5/7 and 1/2. 5 7 and 1 2 are incomplete and confusing.
On Saturday the distance traveled was 5/7 of the total distance.
2/7 of that total was left for Sunday. Half of 2/7 is 1/7.
1/7 of the total distance was traveled on Sunday.
PLE HELP ASAP
WILL MAKR BRAINLIEST
Answer:
no
Step-by-step explanation:
bc in order for the size of a pack to be represented as the function of ots price, you need to have the same ratio for every pack
but if you do the math
2.30/1000=0.0023
1.70/850=0.002
they do not have the same ratio
so no
Identify the vertex and axis of symmetry of the graph of g(x) = |x|- 8
The vertex of the absolute function g(x) = |x|- 8 lies at (0,-8).
What is an absolute function?The absolute value or modulus of a real number x, denoted by |x|, is its non-negative value regardless of its sign.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the absolute function is g(x) = |x| - 8. The vertex will be calculated by plotting the function on the graph.
From the graph, the vertex of the absolute function lies at the point ( 0,-8). The graph is attached with the answer below.
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A certain region of America with over 500,000 households has a mean household income of $70,000 with a standard deviation of $20,000. Economists plan to take random samples of 625 households and calculate the sample mean income for each sample. Calculate the mean of the sampling distribution of x-bar.
Answer: Mean: 70,000
Standard Deviation: 500
Step-by-step explanation:
The mean is 70, 000 and standard deviation is 800.
What is Standard Deviation?The term "standard deviation" (or " σ ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Given:
A certain region of America with over 500,000 households.
Mean, [tex]\mu[/tex] = 70,000
and, Standard Deviation, [tex]\sigma[/tex] = 20,000
n = 625
So, the new mean = old mean
= 70, 000
and, the standard deviation = [tex]\sigma /[/tex]√n
= 20,000 / √625
= 20,000 / 25
= 800.
Hence, the mean is 70, 000 and standard deviation is 800.
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Which of the following numbers has the smallest value?
19.45
19.445
19.5
19.454
Answer:
19.445
Step-by-step explanation:
PLEASE HELP, THIS IS DUE IN 20 MINUTES
Given the following proportion, solve for the length of the triangle "n".
n/4 = 12/(n-2)