log16^*+log4^*+log2^*=7​

Answers

Answer 1

Answer:

[tex]x = 16[/tex]

Step-by-step explanation:

Given

[tex]log_{16}(x) + log_4(x) + log_2(x) = 7[/tex]

Required

Solve for x

[tex]log_{16}(x) + log_4(x) + log_2(x) = 7[/tex]

Change base of 16 and base of 4 to base 2

[tex]\frac{log_2(x)}{log_2(16)} + \frac{log_2(x)}{log_2(4)} + log_2(x) = 7[/tex]

Express 16 and 4 as 2^4 and 2^2 respectively

[tex]\frac{log_2(x)}{log_2(2^4)} + \frac{log_2(x)}{log_2(2^2)} + log_2(x) = 7[/tex]

The above can be rewritten as:

[tex]\frac{log_2(x)}{4log_22} + \frac{log_2(x)}{2log_22} + log_2(x) = 7[/tex]

[tex]log_22 = 1[/tex]

So, we have:

[tex]\frac{log_2(x)}{4*1} + \frac{log_2(x)}{2*1} + log_2(x) = 7[/tex]

[tex]\frac{1}{4}log_2(x) + \frac{1}{2}log_2(x) + log_2(x) = 7[/tex]

Multiply through by 4

[tex]4(\frac{1}{4}log_2(x) + \frac{1}{2}log_2(x) + log_2(x)) = 7 * 4[/tex]

[tex]log_2(x) + 2}log_2(x) + 4log_2(x) = 28[/tex]

[tex]7log_2(x) = 28[/tex]

Divide through by 7

[tex]\frac{7log_2(x)}{7} = \frac{28}{7}[/tex]

[tex]log_2(x) = 4[/tex]

Apply the following law of logarithm:

If [tex]log_ab = c[/tex] Then [tex]b = a^c[/tex]

So, we have:

[tex]x = 2^4[/tex]

[tex]x = 16[/tex]


Related Questions

The price of an item has been reduced by 45%. The original price was $85.

Answers

Answer:

$38.25

Step-by-step explanation:

Answer:

Sale Price: $85 * 0.55 = $46.75

Step-by-step explanation:

Which of the following

Answers

Answer:

A

Step-by-step explanation:

1. Explain the difference between circumscribed angles and inscribed angles in relationship to a circle.

2. Explain, in your own words, the steps required to convert any equation of a circle into standard form be completing the square.

3. Explain/define the following terms, or draw a picture and label the terms.
a. radius
b. diameter
c. chord
d. secant
e. tangent
f. point of tangency

Answers

9514 1404 393

Explanation:

1. Consider the attachment. Angle CDF is a circumscribed angle. It is formed at the intersection of two tangents to the circle. Angles BCE, CBE, and BEC are inscribed angles. Their vertices are on the circle, and they are formed by two chords.

If a chord degenerates to zero length, the ray it represents with respect to an inscribed angle becomes a tangent. That is, angles BCD and ECD can also be considered to be inscribed angles. Similarly, straight angle DFG at tangent point F can be considered to be a degenerate case of both an inscribed angle and a circumscribed angle. (Some authors may not include degenerate cases in their definitions. YMMV)

__

2. The general form of the equation of a circle is ...

  Ax² +Ay² +Dx +Ey +F = 0

Any equation of a circle can be put in this form. If we divide by A, this can be written as ...

  x² +y² -2hx -2ky +c = 0 . . . . where h = -D/(2A), k = -E/(2A), c = F/A

and the equation can be further transformed to the standard form ...

  (x -h)² +(y -k)² = r² . . . . . where r² = h² +k² -c

The last equation is the result of "completing the square" by adding h² and k² to both sides of the second equation shown. The values of h and k are as shown above, given the coefficients of the general form equation.

__

3. Again refer to the attached diagram.

a) a radius is a line segment with the circle center at one end and a point on the circle at the other end. AB and AC are radii.

b) A diameter is a line segment whose ends are on the circle and whose midpoint is the center of the circle. BC is a diameter.

c) A chord is a line segment whose end points lie on the circle. BC, BE, and CE are chords.

d) A secant is a line containing two points of the circle. Lines CG and CE are secants.

e) A tangent is a degenerate case of a secant in which the two points of intersection merge to one point of intersection. It is a line that touches the circle at exactly one point, the point of tangency. DG and DC are tangents.

f) The point of tangency is the single point where a tangent intersects a circle. A radius to the point of tangency (such as AC) is always perpendicular to the tangent line (DC).

Answer the question for brainliest.
(Simplify Please)

Answers

[tex]1 \frac{2}{5} m - \frac{3}{5} ( \frac{2}{3} m + 1)[/tex]

[tex]\frac{7}{5} m - \frac{6}{15} m - \frac{3}{5} [/tex]

[tex] \frac{21}{15} m - \frac{6}{15} m - \frac{3}{5} [/tex]

[tex]( \frac{(21 - 6)m}{15} ) - \frac{3}{5} [/tex]

[tex] \frac{15}{15} m - \frac{3}{5} [/tex]

[tex]1m - \frac{3}{5} [/tex]

[tex]m - \frac{3}{5} [/tex]

10 is 25% of what number?

Answers

Answer:

40

Step-by-step explanation:

A store is on sale for 75% less than it’s original price of $24

Answers

Answer:

So wouldn't  it be like $6 as the actual price now.

Step-by-step explanation:

Hope this helps if not let me know.

Sorry if it is wrong,

please help :)

translate the sentence into an inequality.

two subtracted by Y is less than or equal to -22

Answers

Hope this helps :) the sign might be a little wacky but you get it right?

2/10 (4/5)-(5/2)+ (10)

Answers

Answer:

2/10 (4/5)-(5/2)+ (10)=7.66

Answer:

[tex]\frac{383}{50} = 7.66[/tex]

Step-by-step explanation:

[tex]\frac{2}{10}(\frac{4}{5})-(\frac{5}{2})+10[/tex]

[tex]= \frac{4}{25} -\frac{5}{2}+10[/tex]

[tex]=\frac{383}{50} = 7.66[/tex]

Is a triangle whose sides measure 6 10 and 8 a right triangle?

Answers

Answer:

Step-by-step explanation:

They are equal, and thus, the triangle is a right triangle. ... These sides are 6: 8: 10, then the triangle is a right one.

Priving all night. Kathryn drove her rig 5 hours before
dawn and 6 hours after dawn. If her average speed was
5 miles per hour more in the dark and she covered
630 miles altogether, then what was her speed after dawn?

Answers

Answer:

yes

Step-by-step explanation:

Answer: x=16

Step-by-step explanation:

shown in screenshot below

The fraction 7/8 produces a repeating decimal.
0.875
O A. True
O B. False

Answers

False, the answer is exactly 0.875

Answer:

b

Step-by-step explanation:

the answer to 7/8 is 0.875 it is not recurring as it has no dot at the top

The discrimination of a quadratic function is 13. Which is a true statement about the roots of the function?​

Answers

Answer:

If the discrimination of a quadratic function is 13, then the function will have two distinct real roots.

Step-by-step explanation:

Given the quadratic function

[tex]y=ax^2+bx+c[/tex]

where D = b²-4ac is called the discrimination of a quadratic function.

The discriminant D=b²-4ac indicates the type of roots the equation may have.

If D > 0, then the equation has two distinct real roots.

Given that the discrimination of a quadratic function is 13.

i.e. D = 13

As D > 0, so the function will have two distinct real roots.

Thus, we conclude that if the discrimination of a quadratic function is 13, then the function will have two distinct real roots.

What is 6/7 divided by 2/7

Answers

Answer:

3

Step-by-step explanation:

6/7 divided by 2/7

=

6/7 divide 7/2 (cancel out 7)

=

6 multiply 1/2 (reduce)

=

3

What is the common difference between successive terms in the sequence?
2, 8, 14, 20, 26, ...
-6
-4
4
6

Answers

6
If you subtract it from two or 14 from eight or 24 or 26 for 20 can all see that they are subtracted by six
2 4 6 8 10 12 14 16

Please help my sister is being super mean and my parents are working please help
Which statement is true about the points shown on the number line?
A)-3.8 1.5, and -3.8 is located to the right of 1.5.
D)-3.8 > 1.5, and -3.8 is located to the left of 1.5.

Answers

Answer:

2nd option on the top right

Step-by-step explanation:

tell your sister she sucks for not helping you ;)

A student forgets to study for an exam consisting of ten multiple choice questions, each with three possible answers. Instead, the student will have to randomly guess, so that there is a 1 3 probability of getting any arbitrary question right. If 6 or more correct answers is a passing score, what

Answers

Complete question :

A student forgets to study for an exam consisting of ten multiple choice questions, each with three possible answers. Instead, the student will have to randomly guess, so that there is a 1 3 probability of getting any arbitrary question right. If 6 or more correct answers is a passing score, what is the probability of passing

Answer:

0.07656

Step-by-step explanation:

Given that:

P(correct guess) = 1/3 ; p= 0.33333

Number of questions /trials = 10

P(x ≥ 6) = p(6) + p(7) + p(8) +... + p(10)

This is the sum of the probabilities of getting exactly 6, 7, 8, 9 or 10 questions.

Using the binomial probability calculator to save computation time :

P(x ≥ 6) = 0.07656

5. If AABC = ADEF, find the measure of

Can someone explain me?

Answers

Answer:

Option A) angle B = 67°

Step-by-step explanation:

I'll use " [ " symbol for saying angle.

Alright so ...

since triangle ABC and triangle DEF are congruent

it means [ A = [ D

[ B = [ E

[ C = [ F

here [ A = 78° (which means [ D is also 78°)

and ..[ F = 35° (which means [ C is also 35°)

-->So now all you need to know to find [ B is to know the other two angles in the triangle. and thats where ..

you write.. [ A + [ B + [ C = 180° (angle sum property)

78° + [ B + 35° = 180°

113° + [ B = 180°

[ B = 180 - 113

= 67°

I hope that clears the concept , if you have any questions regarding it I'd love to help .

On a coordinate plane, a triangle has points A (negative 5, 3), B (negative 2, 4), C (negative 2, 2).
Triangle ABC is shown on the graph. What are the coordinates of the image of point B after the triangle is rotated 270° about the origin?

(4, 2)
(2, 4)
(–4, –2)
(–2, –4)
In the diagram, the length of segment QV is 15 units.

Line m is a perpendicular bisector of line segment S Q. It intersects line segment S Q at point R. Line m also contains points T and V. Line segment T S is 3 x + 2. Line segment S V is 4 x minus 1.
What is the length of segment TQ?

4 units
11 units
14 units
15 units

Answers

14 units did it and got it right

(Giving brainliest!!)

Terrance packs two boxes inside a crate. The total weight of the crate and two boxes is 98.45 pounds. One box weighs 32.8 pounds, and the other box weighs 39.34 pounds. How much does the crate weigh?

A) 72.14 pounds
B) 59.11 pounds
D) 26.31 pounds

Answers

Answer:

the crate weighs 26.31

Step-by-step explanation:

add 32.8 and 39.34 together and then subtract 98.45 from the sum. ^^

Answer:

the crate weighs 26.31

Step-by-step explanation:

add 32.8 and 39.34 together and then subtract 98.45 from the sum. ^^

Step-by-step explanation:

Find the measure of the exterior angle.

Answers

add the two angles withen the triangle and make that equal to the exterior angle

Solve the inequality. 4(x + 3) − 7 ≥ x + 3(x + 1)

Answers

Answer:

if want to know is true or flas. this is true

Step-by-step explanation:

It costs $6 to buy 3 bags of chips. How much do 24 bags of chips cost?

Answers

Answer:

$48

Step-by-step explanation:

24/3 = 8

8 x 6 = $48

Answer:

48

Step-by-step explanation:

because butterfly method 6 time 24 =144 and didved 144 by 3 which gives you 48

During the election for class president, 35% of students voted for Leandro and the rest voted for Gerardo. If 70 students voted for Leandro, how many voted for Gerardo? Someone answer it's due tmrw

Answers

Answer:

130 students

Step-by-step explanation:

Out of the whole class, if 35% of students voted for Leandro voted for Leonardo , this means that 64% of the class voted for Gerardo.

Let the total number of people in the class be x;

If 70 students voted for Leandro, then;

35% of x = 70

0.35x = 70

x = 70/0.35

x = 200

The total number of people that voted for Gerardo will be 200 - 70 = 130

Hence 130 voted for Gerardo

What is the zero of the function below?

A. x = -3

B. x = 1

C. x = -1

D. x = 9

Answers

The answer to your question is d
The answer is D hope that helps

Sandra's Bike Club had 360 members last month. Each member pays a $12 membership fee per month.
This month, 27 new members joined and 34 members left the club. How much money will Sandra collect
this month in membership fees?

Answers

Answer:

$4,236

Step-by-step explanation:

34-27=7

360-7=353

353(12)=4,236

What is the measure of eg?

Answers

I’m only in 6th grade

Maria Invests $600 in a bank account that earns simple interest. She earns $30 at the end of 12 months . Janae invest $350 at the same rate of interest for 12 months​

Answers

Answer:

Interest = $1.75

Step-by-step explanation:

Maria invest $600, and receives interest of $30 per year

We know that PRT/100= INTEREST

R=( 100*INTEREST)/(PT)

R = (100*30)/(600*1)

R= 3000/600

R= 5%

Jane invest $350 at Sam rate with Maria , that is 5% , for a year, her interest

Interest= 350*5*1/100

Interest = $1.75

Please help me with this.

Answers

it takes 12 minutes to fill the bathtub!!

hope this helps ;))

Which statement is not true about the pattern sown?

Answers

Answer:each fraction is greater than the one before it is not true

Source:trust me bro

The one that is highlighted

17 increased by twice Greg's height

Answers

Answer:25

Step-by-step explanation:

Kind of need more information to answer....
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