Solving Logarithmic Equations

Identify the solution set of 3 In 4 = 2 In x.
o {6}
O {-8, 8}
o {8}
DONE
(8)

Answers

Answer 1

Answer:

Step-by-step explanation:

3ln(4) = 2ln(x)

ln(4³) = ln(x²)

4³ = x²

(2²)³ = x²

2⁶ = x²

x = ±√2⁶ = ±2³ = ±8

However, the argument of a logarithm must be positive, so x=8.

Answer 2

The solution set of the equation is {8, -8}, but we can discard the negative solution as it is not physically meaningful in this context. So, the final solution set is {8}. Option D is correct.

To solve the equation, we can use the logarithmic identity that states:

n * log(a) = log(aⁿ)

Using this identity, we can rewrite the equation as:

In(4³) = In(x²)

Simplifying both sides using the natural logarithm properties, we get:

In(64) = In(x²)

Taking the exponential of both sides, we have:

[tex]e^{In 64} = e^{In x^2}\\64 = x^2[/tex]

Taking the square root of both sides, we get:

x = ±8

However, we must check if either of these solutions makes the argument of the natural logarithm negative, which is not allowed. Since the argument of the natural logarithm is positive for both x = 8 and x = -8, both solutions are valid.

Therefore, the solution set of the equation is {8, -8}, but we can discard the negative solution as it is not physically meaningful in this context. So, the final solution set is {8}.

Learn more about logarithmic function here:

https://brainly.com/question/3181916

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Related Questions

(6n – 7) + (8n + 2) = 23

Answers

Answer:100

Step-by-step explanation:

2!2

Answer:

n = 2

Step-by-step explanation:

(6n - 7) + (8n + 2) = 23 (Combine like terms)

14n  - 5 = 23 (Add 5 from both sides)

14n = 28 (divided 14 from both sides)

n = 2

Fill in the box to rewrite the expression 5x + 10
using the GCF.
5x + 10 = (
x) + (5 •

Answers

The GCF is 5 so the new expression would be: 5(x+2)

the segment joing C and D (-0.6, -0.8) is the tangent to the unit circle at D. what is the exact value of...

1. sin(t - 2pi)

2. tan(t + pi)

3. tan(t - 2pi)​

Answers

Answer:

Tan(t+pi) = 3

Step-by-step explanation:

First let's find the slope of the line through the points  and  

Note:  is the first point . So this means that x%5B1%5D=-2 and y%5B1%5D=0.

Also,  is the second point . So this means that x%5B2%5D=0 and y%5B2%5D=3.

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.

m=%283-0%29%2F%280--2%29 Plug in y%5B2%5D=3, y%5B1%5D=0, x%5B2%5D=0, and x%5B1%5D=-2

m=%283%29%2F%280--2%29 Subtract 0 from 3 to get 3

m=%283%29%2F%282%29 Subtract -2 from 0 to get 2

So the slope of the line that goes through the points  and  is m=3%2F2

Now let's use the point slope formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula

 

y-0=%283%2F2%29%28x--2%29 Plug in m=3%2F2, x%5B1%5D=-2, and y%5B1%5D=0

y-0=%283%2F2%29%28x%2B2%29 Rewrite x--2 as x%2B2

y-0=%283%2F2%29x%2B%283%2F2%29%282%29 Distribute

y-0=%283%2F2%29x%2B3 Multiply

y=%283%2F2%29x%2B3 Simplify

So the equation that goes through the points  and  is y=%283%2F2%29x%2B3

Notice how the graph of y=%283%2F2%29x%2B3 goes through the points  and . So this visually verifies our answer.

Graph of y=%283%2F2%29x%2B3 through the points  and

PLEAAASSSEE HELP!! ITS DUE IN 1 HOUR

Answers

Answer:

-4 and +4

Step-by-step explanation:

(- - - -) = -4

(+ + + +) = 4 or +4

-4 and +4 hope this helps

Please give me the correct answer.Only answer if you're very good at math.

What is the relationship between toppings and price?

A:Fornos charges one euro for every topping.

B:Fornos charges one euro for a plain slice, and one-half euro for each extra topping.

C:Fornos charges one and a half euros for each topping.

D:Fornos charges one-half for each topping. ​

Answers

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

If a triangle has side lengths of 28,45, and 50, is the triangle acute,obtuse,or right?

Answers

Answer:

Acute i think

Step-by-step explanation:

Answer:

acute

Step-by-step explanation:

what is x and y? help

Answers

y is Six and x is Ten
Since B is double its size your gonna multiply by 2 so
x would equal 10
And with b your dividing by 2
So y would be 6

pleaseeee Answer! Will Mark as Brainliest for the Best Answer

Answers

p^4 s^5 y^-7 z^-1
................................

Answer:

[tex]p^{4} s^{5} y^{-7} z^{-1}[/tex]

Step-by-step explanation:

[tex]\frac{1}{y^{7} } = y^{-7}[/tex]

[tex]\frac{1}{z} = z^{-1}[/tex]

What is the volume of the prism?



Enter your answer, as a mixed number in simplest form, in the box.


cm³

The figure contains a right rectangular prism. The length of the prism is labeled 6 and one half centimeters, the width is labeled 2 and one half centimeters, and the height is labeled 2 and one half centimeters.

Answers

Answer:

40 [tex]\frac{5}{8}[/tex] [tex]cm^{3}[/tex]

Step-by-step explanation:

The figure is a rectangular prism, so the formula would be Volume = length x width x height.

length =  6 [tex]\frac{1}{2}[/tex] cm

width  =  2 [tex]\frac{1}{2}[/tex] cm

height  =  2 [tex]\frac{1}{2}[/tex] cm

If you plug everything you have in the problem into the volume equation, you would get : Volume = 6 [tex]\frac{1}{2}[/tex] cm x 2 [tex]\frac{1}{2}[/tex] cm x 2 [tex]\frac{1}{2}[/tex] cm.

Without a calculator, I would first turn the mixed numbers into improper fractions.

6 [tex]\frac{1}{2}[/tex]  = [tex]\frac{13}{2}[/tex]2 [tex]\frac{1}{2}[/tex] = [tex]\frac{5}{2}[/tex]

Volume = [tex]\frac{13}{2}[/tex] x  [tex]\frac{5}{2}[/tex] x  [tex]\frac{5}{2}[/tex]

When you multiply everything together you should get [tex]\frac{325}{8}[/tex].

As a mixed number, that would be 40 [tex]\frac{5}{8}[/tex] [tex]cm^{3}[/tex].

You deposit $5,000 in a bank account that earns 4% simple interest. How much interest will you earn in 2 years?

Answers

Answer:

Step-by-step explanation:

triangle similarity i think ... picture included * SIN COS TAN

Answers

Answer:

d = 105tan(37°)

Step-by-step explanation:

opposite (o) = d

adjacent (a) = 105

Angle A = 90 - 53 = 37°

Therefore,

the correct equation would be

tan(A°) = opposite/adjacent

tan(37°) = d/105

d = 105tan(37°) ✅

d = 105 × 0.7535540501

d ≈ 79.12 units

______________

#IndonesianPride

- kexcvi

Can somebody help me? -2-7p<26

Answers

Answer: p>−4

Step-by-step explanation:

Let's solve your inequality step-by-step.

−2−7p<26

Step 1: Simplify both sides of the inequality.

−7p−2<26

Step 2: Add 2 to both sides.

−7p−2+2<26+2

−7p<28

Step 3: Divide both sides by -7.

−7p

−7

<

28

−7

p>−4

Parallel Lines cut by a transversal

Answers

Answer:

110

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Set the two given equations equal to each other (alternate angles i think)

12x + 2 = 11x + 11

**simplify and pull x to one side**

x = 9

**now insert x=9 into one equation (I choose 12x+2**

12(9) + 2 = 108 + 2 =110

A

Write an equivalent expression in word form.

(1- 1/3) / 2

Answers

Answer:

21

Step-by-step explanation:

one third taken away from one, halved
or
half of one minus one third

M=-1 and it has a y-intercept of (0,-6). Write the equation that represents the situation.

Answers

Answer:

y=-1x-6

Step-by-step explanation:

do you need a explanation aswell?

Which of the following table of values represent a function?
A. (-1,5) (1,5) (4,5) (-4,5) (1,-5)
B. (1,0) (0,2) (5,-4) (-2,-1) (1,5)
C. (2,2) (3,3) (4,4) (5,5) (6,6)
D. (1,-4) (4,2) (-4,0) (0,3) (-4,-2)

Answers

C is the answer

Step-by-step explanation:

but I think is C

6. Ria purchased a car for
$14,775. Sales tax in her
county is 6.8%.
a. What is the total price of
the car including tax?

b. If she puts $2,100 down,
how much will she be
financing?

c. What will her monthly
payment be if the term of
the loan is 72 months with
an APR of 3.5%?

Answers

9514 1404 393

Answer:

  a) $15,779.70

  b) $13,679.70

  c) $210.92

Step-by-step explanation:

a) When tax is added, the total cost is ...

  total = price × (1 +tax rate)

  total = $14,775 × 1.068 = $15,779.70

__

b) The amount financed is the difference between the total cost and the down payment.

  financed = total - down35

  financed = $15,779.70 -2100 = $13,679.70

__

c) The monthly payment is found using the amortization formula. It can also be found using any of a number of financial calculators, spreadsheets, or apps.

  A = P(r/12)/(1 -(1 +r/12)^-n) . . . . annual rate r, n monthly payments, principal P

  A = $13,679.70(0.035/12)/(1 -(1 +0.035/12)^-72) ≈ $210.92

what 2 numbers can be added to make -40 as well as added to make -6?

Answers

-20 x 2 or -10 x 4 both equal -40

-2 x 3 = 6

The temperature at 5:00 am functions

Answers

Answer:

t2 =  37 °F

Step-by-step explanation:

t

1

=52

F

g=3

F/hr

Factor the GCF out of each term of the polynomial.

Answers

Answer For The Number 22: Factors of 22 are 1, 2, 11, 22. There are 4 integers that are factors of 22. The greatest factor of 22 is 22. 3.

Answer For The Problem 2x3 (Divide it by the numbers I give you meaning divide the number two by what I give yo and the other number 3 by it.

The common factors for 2,3 are −1,1 . The numbers do not contain any common variable factors. The GCF (HCF) of the numerical factors −1,1 is 1 .The number is one.

Answer For The Problem 2x5 is also 1 so decide both 2&5 by 1 then multiply. After doing that for answers 2&3 add them. last if you then subtract 22 that might be the answer so put that & also put the answer of the greatest common factor of 22 which is 3. Make sure to include that the one where you subtracted 3 was the greatest common factor for 22.

Dare to do this if you are geiness
Express 750×900as a product of it prime factors using exponents
Who did this get a follow and marked as brainliest​

Answers

Answer:

2^3 x 3^3 x 5^4

Step-by-step explanation:

750 x 900 = 675000

675000 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5 x 5

Which in product of prime factors is = 2 to the power of 3 x 3 to the power of 3 x 5 to the power of 4

Please answer this! I need a quick answer with work.

Answers

Equations -

1. Input u!

[tex] \frac{2.6 - ( - 1)}{5.8} [/tex]

Solve the problem!

[tex] \frac{3.6}{5.8} [/tex]

[tex] \frac{3.6}{5.8} =0.62[/tex]

Answer:

0.44827586

Step-by-step explanation:

(2.6)(−1)/-5.8=-2.6/-5.8 so you get 0.44827586

help0000000000000000000

Answers

Answer:

The answer is going to be C.

Step-by-step explanation:

To help you in the future with any question like this one, you can always use Desmos Calculator.

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Question Progress
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Oilsee
Homework Progress -
26 / 28 Marks
D
S
Here is a list of numbers:
20 29 30 33 37 40
41
46
50
Use four of the numbers to make a sequence and describe the rule
for continuing your sequence.
I
equences - Term-to-Term Rule
Overview
0​

Answers

Answer:

20 292 02 202 202

Step-by-step explanation:

In ΔOPQ, the measure of ∠Q=90°, PQ = 1.8 feet, and OP = 7.4 feet. Find the measure of ∠P to the nearest degree.

Answers

Answer:

P=75.922 ≈ 76

Step-by-step explanation:

What function uses the ADJACENT and the HYPOTENUSE?

SOH-CAH-TOA

cos P = adjacent/hypotenuse= 1.8/7.4

Pcos^-1 = (1.8/ 7.4)

P=75.922 ≈ 76

The total population of a town is 128200 if 55% men are find the number of all the six pairs of corresponding
Pls help

Answers

Answer:

Here is the answer bro

Find the unit rate for each Lean Cuisine Entree. Show your
work
Please show work worth 40 points

Answers

Answer: 60

Step-by-step explanation:10 x 6 = 60 ( Also, 6x6x6x6x6x6x6x6x6x6 = 60

plz help asap I'll mark brainliest!!!​

Answers

1280 bc if you multiply 320 by 4 that will be 1280
ANSWER

1280

EXPLINSTION

because

One number is 4 more than another, and their sum is 60. What is the smaller number?



If x = the larger number and y = the smaller number, then which of the following systems could be used to solve the problem?

x + y = 60 and -x + y = 4
x + y = 60 and x + y = 4
x + y = 60 and x - y = 4
Unlimited Attempts Remain

Answers

Answer:

Step-by-step explanation:

The system is

x+y=60 and x-y=4

If we get the difference between the two equations above we get

x+y-x+y=60-4

2y=56

y=28

If f(x)=3x+2, what is f(3)-7

Answers

Answer:

[tex] \orange{ \bold{f(3) - 7 = 4}}[/tex]

Step-by-step explanation:

[tex]f(x) = 3x + 2 \\ \\ plug \: x = 3 \\ \\ f(3) = 3(3) + 2 = 9 + 2 \\ \\ f(3) = 11 \\ \\ f(3) - 7 = 11 - 7\\ \\ \purple{ \bold{f(3) - 7 = 4}}\\ \\ [/tex]

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