Which of the following shows the extraneous solution to the logarithmic equation log7(3x^3+x)-log7(x)=2?

Answers

Answer 1

Answer:

x=4

Step-by-step explanation:

on edge

Answer 2

The extraneous solution to the logarithmic equation log₇(3x²+x)-log₇x=2 is x=16

What is logarithm?

When you raise a number with an exponent, there comes a result.

Lets say you get[tex]a^b = c[/tex]

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

We are given the function as;

log₇(3x²+x)-log₇x=2

Domian: 3x²+x>0

x(3x+1)>0

x∈(-∞,-1/3)U(0,∞)

Hence, x∈(0,∞), Thus x∈(0,∞)

In this problem we use the following formula:

 [tex]\boxed {log_ax-log_ay=log_a\frac{x}{y}}\displaystyle\\log_7(3x^2+x)-log_7x=2\\\\log_7(x(3x+1))-log_7x=2(1)\\\\log\frac{x(3x+1)}{x} =2(log_77)\\\\log(3x+1)=log_77^2\\\\log_7(3x+1)=log_749\\\\\\\\3x+1=49\\\\3x+1-1=49-1\\\\3x=48\\\\x=16[/tex]

Learn more about logarithm here:

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Related Questions

add my sc tregan_fought

Answers

are you old???????????

Write the ratio as a fraction in simplest from 2ft to 30 in

Answers

Step-by-step explanation:

please please complete it ​

Answers

Answer:

1. 14

2. 11

3. 19.5

4. 16

5. 76

6. 10

7.  2.5

8. 4.5

9. Mean: 10, Median: 9, Mode: 7

10. Mean: 6, Median: 7, Mode: 8,5

11. Mean: 10, Median: 11.5, Mode: 12

Step-by-step explanation:

a function may assign the same output value to two different input values

Answers

this is true i i i i i i i i i i i i

In a new movie
theatre, seats will
be installed in the
unshaded area
How many square
feet are available
for seats?

Answers

Answer. 655.4

Step-by-step explanation:

what did u get?

Da Baby has $45,000 and earns $2,500 each hour
from streams. JoJo Siwa has $62,000, earns $2,000
each hour from streams.
How
SI
Each equation represents the amount in the bank after
t hours.


Da Baby: s= 2,500t + 45,000
JoJo Siwa: s= = 2,000t + 62.000
How many hours, will it take for Da Baby and JoJo
Siwa to have the same amount in the bank?

Answers

Answer:

Step-by-step explanation:

maybe 30 vtfyubf6tyubtfcgnfgghghnvb ngvbhfhgbfvgn

How many terms? 7y-4+3f+6t

PLs I am doing a quiz

Answers

Answer:

B

Step-by-step explanation:

Answer:Only 1 term because the others are coefficients because they have a variable by them.

if the temperature at the North Pole is -10º F, how many degrees would the temperature have to increase for it to be 0º?

Answers

Answer:

10 degrees

Step-by-step explanation:

:) Thank you enjoy your day kind human :)

Answer:

10.

Step-by-step explanation:

-10 + 10 = 0.

works the same for degrees as well.

In a particular lottery, 5 winning numbers are drawn from a set of 37 numbers. What is the probability of picking exactly 2 of the winning numbers in this lottery? Round your answer to the nearest
thousandth (three decimal places).

Answers

Since 5 winning numbers are draw and there are exactly 2 winning numbers, the other 3 numbers chosen have to be incorrect.

The 2 numbers picked right, there are 5C2=10 different possibilities.

The other 3 numbers are just picked from the rest of the 32 numbers. Getting there are 32C3=4960 different possibilities.

For each set of 2 correct winning numbers, you could have the 4960 different losing numbers to match up to make a unique set. This meant that there are 4690*10=46900 different total possibilities.

Now the total different outcomes of how you can choose the numbers are 37C5=435897 outcomes.

Now the way to find probabilities is want/total

The want is 46900 and the total is 435897

Doing the division you get the number rounded to the nearest thousandths as   0.107 or in percent form as

10.759% chance of picking exactly 2 winning numbers.

This seems like a competition problem of some sort therefore I assume that you already know what combinations in form nCk and permutation in form nPk means.

A study was conducted to investigate whether the mean price of a dozen eggs was different for two different grocery stores, Store A and Store B, in a large city. A carton of one dozen eggs from each store was randomly selected for each of 35 weeks, for a total sample size of 35 cartons from each store. The mean price of the 35 cartons was recorded for each store. The difference in the mean carton price for the stores will be calculated.

Which of the following is the appropriate test for the study?

A one-sample z -test for a population proportion

A one-sample t -test for a sample mean

A matched-pairs t -test for a mean difference

A two-sample t-test for a difference between population means

A two-sample z-test for a difference between population proportions

Answers

Answer:

A two-sample t-test for a difference between population means

Step-by-step explanation:

Answer:

D) A two-sample  t -test for a difference between population means

Step-by-step explanation:

Two random samples are selected on a quantitative variable, and the difference in the sample means will be calculated. The appropriate test is the two-sample t-test for a difference in population means.

24 is what percent of 60​

Answers

Answer: 14.4

Step-by-step explanation:

60 * (24/100) = 14.4

(2) Mai walked 1/8 of a 30-mile walking trail. How many miles did Mai walk? Explain or show your reasoning. *​

Answers

Answer: 3.75 miles

Step-by-step explanation:

Divide 30 by 8. 30/8= 3.75. If she walked 1/8 then she walked 3.75 miles

Jean junction is selling jeans at 12% off the regular price. The regular price is $32.00 per pair. What is the discount amount

Answers

Discount amount is 3.75 I think!

Help!!!!!! Please I have no idea what this is!!!

Answers

Answer:

33.49 cubic units

Step-by-step explanation:

[tex]V_{sphere} = \frac{4}{3} \times \pi {r}^{3} \\ \\ V_{sphere} = \frac{4}{3} \times \pi {(2)}^{3} \\ \\ V_{sphere} = \frac{4}{3} \times \pi \times 8 \\ \\ V_{sphere} = \frac{32 \times 3.14}{3} \\ \\ V_{sphere} = \frac{100.48}{3} \\ \\ V_{sphere} = 33.4933333\\ \\ V_{sphere} \approx 33.49\: units^3 [/tex]

Easy math question! Just need to subtract, help out ASAP!

Answers

Answer:

14,599

Step-by-step explanation:

what is the area of circle if diameter is 6feet

Answers

Answer:

Area=πr²

=3.14×(6/2)²

=28.26 ft²

Step-by-step explanation:

find the value of x in each triangle with the given angle measures ​

Answers

Answer:

10 - 104

11 - 25

12 - 64

13 - 109

14 - 33

15 - 90

Step-by-step explanation:

For the first 3 triangles u must add the two angles and minus it from 180

Q number 13 do the same thing then minus the number u got by 180

Q number 14 .... 66 - 180 = 33

Q number 15 it is a right angle so it is 90

Two linear functions are shown.
Which function has the greater
initial value?
Function B
y = 6x + 3
Function A
Х y
- 1 9
0 6
1 3
2 0
Function has the greater initial value because the initial value for Function A is and the initial
value for Function B is
(Type integers or decimals.)
Enter your answer in the edit fields and then click Check Answer.
All parts showing

Answers

Answer:

Function A has a greater initial value because the initial value for Function A is 6 and the initial vale for Function B is 3

Step-by-step explanation:

The data for Function A is presented here as follows;

[tex]\begin{array}{cc}x&y\\-1&9\\0&6\\1&3\\2&0\end{array}[/tex]

The slope of the function, 'm', is given using any two points as follows;

m = (9 - 3)/((-1) - 1) = -3

The slope of the function = -3

The equation of function in point and slope form is given as follows;

y - 3 = -3·(x - 1)

The equation of Function A, is therefore, given as follows;

y = 3 - 3·x + 3 = 6 - 3·x

∴ y = 6 - 3·x

The equation of Function B is given as follows;

y = 6·x + 3

The initial value of a function is given by the y-intercept of the function, where the input variable (x-variable) is zero

The initial value, (y-intercept) of Function A, f(0) is therefore found as follows;

f(x) = y = 6 - 3·x

f(0) = 6 - 3×0 = 6

The initial value of Function A, f(0) = 6

Similarly, the initial value, (y-intercept) of Function B, f(0) is found as follows;

f(x) = y = 6·x + 3

f(0) = 6×0 + 3 = 3

The initial value of the Function B, f(0) = 3

Therefore, we have that Function A has a greater initial value than Function B

Please help! I filled in a little circle bc i thought it was right XDD

Answers

That’s correct, as you’re reversing the positive on both sides for that number. Nice!
1st one is right.

The 4th and 2nd ones are obviously wrong. And the 3rd one is wrong too because you can’t add 3 1/5, because your trying to get rid of it.

Trigonometry help finding the value of x

Answers

Answer:

[tex]5\sqrt{3}[/tex] or 8.66

Step-by-step explanation:

use tan:

tan = [tex]\frac{opposite}{adjacent}[/tex]

⇒ tan 60 = [tex]\frac{x}{5}[/tex]

tan of 60 is 1.73

⇒ 1.732 = [tex]\frac{x}{5}[/tex]

multiply 5 on both sides

⇒ 1.732 x 5 = [tex]\frac{x}{5}[/tex] x 5

⇒ 8.66

Answer:

[tex]\boxed {\boxed {\sf D. \ 5 \sqrt 3 \ or \ 8.66}}[/tex]

Step-by-step explanation:

Remember the 3 main trigonometric ratios:

sinθ= opposite/hypotenuse cosθ= adjacent/hypotenuse tanθ= opposite/adjacent

We are given the 60 degree angle. 5 is adjacent to the angle and x is opposite. Therefore, we must tangent.

[tex]tan \theta= \frac {opposite}{adjacent}[/tex]

[tex]tan60=\frac {x}{5}[/tex]

Since we are solving for x, we must isolate that variable. It is being divided by 5 and the inverse of division is multiplication. Multiply both sides by 5.

[tex]5(tan60)=\frac {x}{5} *5[/tex]

[tex]5(tan60)=x\\5*$$1.73205080757= x\\8.66025403784=x[/tex]

If we round to the nearest hundredth, the 0 in the thousandth place tells us to leave the 6.

[tex]8.66 \approx x[/tex]

x is about 8.66 or 5√3, which is choice D.

please help with explanation and show work :)

Answers

3. A=bh/2
2A=bh
h=2A/b.

8. Dy-Cx=E
Dy=E+Cx
y=(E+Cx)/D

please help me, i'll mark you brainiest
20 points

Answers

Answer: 4! 300:75     Hope you have a great day! Good luck on any stressful school homework stuff you have today too!

Step-by-step explanation: A fraction consists of two numbers and a fraction bar:

300/75

The number above the bar is the numerator: 300

The number below the bar is the denominator: 75

Divide the numerator by the denominator to get fraction's value:

300/75 =

300 ÷ 75 =

4:1

A shipping and handling free 35.00 is charged to all furniture over $250 if the order is $437.50 what percent is the shipping and handling free?

Answers

Answer:

8%

Step-by-step explanation:

Divide 35 and 437.50 and you get 0.8

Then multiply .8 times 100 = 8%

the other person is correct give brainliest

what is the volume???

Answers

Answer:

that would be 80

Step-by-step explanation:

Here it is

I need help with it ​

Answers

Answer:

variable, variable, known, unknown

Step-by-step explanation:

Put the following equation of a line into slope-intercept form, simplifying all fractions. x + 2y = 16​

Answers

Answer:

x + 2y = 16

The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

y=mx+b

Rewrite in slope-intercept form.

y= −1/2x+8

Step-by-step explanation:

Hope it is helpful...

Hey there!

The answer is y = [tex]\frac{-1}{2}[/tex]x + 8

To put it into slope-intercept form, we must get "y" by itself on one side of the equation. First, to do this, we will subtract "x" from both sides.

2y = -x + 16

Lastly, we divide both sides by 2

y = [tex]\frac{-1}{2}[/tex]x + 8

Have a super awesome day! :)


Pleaseee hurry and help

Answers

Answer: 37. 7in

12*3.14= 37.68

Rounded= 37.7 inches

Which equation represents a line passing through the point (8, 9) with a slope of 3?

Answers

The equation of a line passing through the point (8, 9) with a slope of 3 is y = 3x - 15.

What is the equation of a line passing through two given points in 2-dimensional plane?

Suppose the given points are [tex](x_1, y_1) and (x_2, y_2),[/tex]

then the equation of the straight line joining both two points is given by

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

We have been given a line passing through the point (8, 9) with a slope of 3.

then the equation of the straight line joining both two points is given by

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

Its slope would be:

[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

m = 3

Therefore, the equation of the straight line

[tex](y - 9) = 3 (x -8)\\\\y - 9 = 3x - 24\\\\y = 3x -15[/tex]

Hence, the equation of a line passing through the point (8, 9) with a slope of 3 is y = 3x - 15.

Learn more about straight-line equations here:

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Find the smallest number such that the remainder is 3 when it is divided by 16,20 or 24.​
(step required,thank you)

Answers

Answer: 123

Step-by-step explanation:

Foe us to solve this, we have to find the lowest common multiple of 16, 20 and 24 first and then add 3 to the LCM. This goes thus:

Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160

Multiples of 20 = 20, 40, 60, 80, 10, 120, 140, 160

Multiples of 24 = 24, 48, 72, 96, 120

Therefore, the Lowe's common multiple is 120.

We then add the remainder of 3 and this will give:

= 120 + 3

= 123

7/9 - something = 2/9

Answers

Answer:

5/9

Step-by-step explanation:

Answer:

5/9

Step-by-step explanation:

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