What is the value of x if e^3x+6 =8? Answer:

Answers

Answer 1

Answer:

[tex]\displaystyle x = \frac{ln2}{3}[/tex]

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Algebra II

Natural logarithms ln and Euler's number eLogarithmic Property [Exponential]:                                                                [tex]\displaystyle log(a^b) = b \cdot log(a)[/tex]Solving logarithmic equations

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle e^{3x} + 6 = 8[/tex]

Step 2: Solve for x

[Equality Property] Isolate x term:                                                                   [tex]\displaystyle e^{3x} = 2[/tex][Equality Property] ln both sides:                                                                    [tex]\displaystyle lne^{3x} = ln2[/tex]Rewrite [Logarithmic Property - Exponential]:                                                [tex]\displaystyle 3xlne = ln2[/tex]Simplify:                                                                                                             [tex]\displaystyle 3x = ln2[/tex][Equality Property] Isolate x:                                                                            [tex]\displaystyle x = \frac{ln2}{3}[/tex]
Answer 2

Answer:

x = 1/3 ln(2) or approximately 0.23104

Step-by-step explanation:

e^3x+6 =8

Subtract 6 from each side

e^3x+6-6 =8-6

e^3x =2

Take the natural log of each side

ln( e^3x) =ln(2)

3x = ln(2)

divide by 3

3x/3 = 1/3 ln(2)

x = 1/3 ln(2)

x is approximately 0.23104


Related Questions

3 different problems.

solve b - 4 = 3.

solve -32 = 8w

solve n
— = -4
7

Answers

Answer:

see below

Step-by-step explanation:

b - 4 = 3

Add 4 to each side

b - 4+4 = 3+4

b = 7

-32 = 8w

Divide by 8

-32/8 = 8w/8

-4 = w

n/7 = -4

Multiply by 7 to each side

n/7 *7 = -4*7

n = -28

Answer:

1. b = 7

2. w = -4

3. n = -28

Step-by-step explanation:

1. b - 4 = 3

Tip: Whenever there’s a number being subtracted or added, it’s best to make that number a 0

Step 1. Add 4 to both sides

b - 4 = 3

b + 4 = +4

b = 7

—————————————
2. -32 = 8w

Step 1. Isolate the variable
(by dividing both sides by 8)

w = -32/8

w = -4

—————————————
3. n/7 = -4

Step 1. Multiply 7 x -4

n = -28

solve A = 1/2bh, for b

Answers

Answer:

b=2A/h

Step-by-step explanation:

First I throw everything else to another side with A by dividing them

(A = b)/2h

then I get

b=2A/h

Step-by-step explanation:

A = 1/2 bh

divide by 1/2

2A = bh

divide by h

2A/h = b

I need help I need help

Answers

Answer:

[tex]{ \boxed{ \bf{c}}} \: \: \frac{3.8}{4} = s[/tex]

Step-by-step explanation:

[tex]{ \tt{4 \: pies \: = \: 3.8 \: ounces}} \\ { \tt{1 \: pie \: = \: ( \frac{1}{4} \times 3.8) \: ounces}} \\ { \tt{ = 0.95 \: ounces}}[/tex]

[tex]{ \underline{ \sf{ \blue{christ \: † \: alone}}}}[/tex]

what are examples of like terms

Answers

Answer:

7x and 2x. 3x^2 and -7x^2.

Step-by-step explanation:

7x and 2x both have x. 3x^2 and -7x^2 both have x^2.

Write 0.0406 in scientific notation.

Answers

Answer:

4.06×10^-2

hope that helps uh..☺

Answer:

Ans; 0.0406 = 4.06 ×10–²

(4a)^2 without the exponents

Answers

Answer:

16 a*a

Step-by-step explanation:

(4a)^2

(4a) (4a)

16 a*a

Answer:

16a²

Step-by-step explanation:

(4a)²

=>(4)² x (a)²

=> 16 x a²

=>16a²

Alvin’s first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by –3. Which linear combination of Alvin’s system of equations reveals the number of solutions to the system?

9x + 4y = 36

6x + 2.5y = 24

Infinite solutions: 0x – 0y = 0
No solutions: 0x + 15.5y = 144
One solution: 0x + 0.5y = 0
Two solutions: 0x – 0.5y = 60

Answers

Answer:

One solution: 0x + 0.5y = 0

Step-by-step explanation:

9x + 4y = 36

6x + 2.5y = 24

2 * Eq. 1

18x + 8y = 72

-3 * Eq. 2

-18x - 7.5y = -72

Add the multiples of the equations.

0x + 0.5y = 0

Answer: One solution: 0x + 0.5y = 0

The linear combination that reveals the number of solutions to the system is as follows:

One solution: 0x + 0.5y = 0

The system of linear equation is as follows:

9x + 4y = 36

6x + 2.5y = 24

He multiplied the first equation by 2 and the second equation by –3. Therefore,

Combined equation:

18x + 8y = 72

-18x - 7.5y = -72

Therefore, let's add the equation

0x + 0.5y = 0

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Can the sides of a triangle have lengths of 42, 45, and 13? If so, what kind of triangle is it?

Answers

Answer:

obtuse

Step-by-step explanation:

45^2 = 2025

42^2 = 1764

13^2 = 169

169+1764=1933

2025 > 1933

therefore it is an obtuse triangle

Twice the sum of x
and 5 equals 3.

Answers

⇛2x + 5 = 3

⇛2x = 5 - 3

⇛2x = 2

⇛x = 2/2

⇛x = 1

Answer:

1

Step-by-step explanation:

What are the coordinates of P?
(b,0
a,0
0,a
0,b

Answers

Answer:

a,0

Step-by-step explanation:

Look at point (a,b). Point (a,b) has the same x-coordinate as P. And then the y coordinate is 0 because it just sits on the x axis and doesn't go up any. Therefore the answer is P: (a,0).

Find the surface area of each figure. Round your answers to the nearest tenth, if necessary​

Answers

Answer: 109m^2

Step-by-step explanation:

(5)(8.4)/2 = 21 m^2

(4 ) (21) = 84 m^2

Base = 5^2 = 25 m^2

84 + 25 = 109 m^2

Full working out for this question please.

Answers

Answer:

d 28.8cm2

Step-by-step explanation:

1/2BH

1/2() 12.8() 4.5

28.8

Brian scored 120 on his test the first time he took the test. The second time he took the test,
he scored 150. By what percentage did Brian increase his score?
a. 20%
b. 25%
c. 80%
d. 125%

Answers

Answer:

b. 25%

Step-by-step explanation:

(new - old)/ old * 100%

150 - 120 = 30 ... 30/120 = .25 * 100% = 25%

Answer:

25% increase

Step-by-step explanation:

Take the new amount and subtract the original amount

150-120

30

Divide this by the original amount

30/120

1/4

.25

Multiply by 100%

25%

Can anyone tell me why by direct substitution of x, the equation (circled ones) equals to the indeterminate form, 0/0? When you can do x²-k=6 something like that​

Answers

Answer:

See explanation and hopefully it answers your question.

Basically because the expression has a hole at x=3.

Step-by-step explanation:

Let h(x)=( x^2-k ) / ( hx-15 )

This function, h, has a hole in the curve at hx-15=0 if it also makes the numerator 0 for the same x value.

Solving for x in that equation:

Adding 15 on both sides:

hx=15

Dividing both sides by h:

x=15/h

For it be a hole, you also must have the numerator is zero at x=15/h.

x^2-k=0 at x=15/h gives:

(15/h)^2-k=0

225/h^2-k=0

k=225/h^2

So if we wanted to evaluate the following limit:

Lim x->15/h ( x^2-k ) / ( hx-15 )

Or

Lim x->15/h ( x^2-(225/h^2) ) / ( hx-15 ) you couldn't use direct substitution because of the hole at x=15/h.

We were ask to evaluate

Lim x->3 ( x^2-k ) / ( hx-15 )

Comparing the two limits h=5 and k=225/h^2=225/25=9.

Find the arc length of the partial circle.

Answers

Answer: C=10.99

Step-by-step explanation:

It can be seen that the arc has an angle of a=90 degrees, respectively, the length of the arc can be found by the formula[tex]\bf C=\dfrac{2\bf {\pi} r}{360} \cdot \alpha=> \dfrac{2\cdot 3,14\cdot 7 }{360} \cdot 90=\boxed{\bf 10.99}[/tex]  

Use the Diagram to find BC.

Answers

Answer:

Step-by-step explanation: you have to ask your parents for help

5 a + 3 b + 2 a b + 4 a -7 b​

Answers

Answer:

5a+4a=9a

3b-7b=-4b

2ab

=9a-4b+2ab or 2ab+9a-4a

Step-by-step explanation:

Calculate liked terms

A sinusoidal graph has an amplitude of 9 and a midline of y = –2. Determine
the range of the graph.

Answers

Answer:

[tex]( - 11.7)[/tex]

Range 18

Step-by-step explanation:

Twice the amplitude.

Geometry, please answer my question ASAP

Answers

Answer:

98 degrees

Step-by-step explanation:

The angles of a quadrilateral add up to 360 degrees, therefore:

(25x+1)+(25x-2)+(20x-1)+82=360

70x +80=360

70x=280

x=4

the angle at C:

25*4-2 = 98 degrees

F(x) = 3x + 2 what if f(5)

Answers

Ans is 17 . Solved it Down below. Hope it help

Write down at least five number pairs to solve the equation vw = 50

Answers

Answer:

1, 50

2, 25

5, 10

10, 5

25, 2

Answer:

Step-by-step explanation:

V  W  

1 x 50     = 50

1.5 x 33 1/3 = 50

2 x 25     = 50

2.5 x 20     = 50

3 x 16 2/3 = 50

3.5 x 14 2/7 = 50

4 x 12 1/2 = 50

4.5 x 11 1/9 = 50

5 x 10     = 50

5.5 x 9     = 50

6 x 8 1/3 = 50

6.5 x 7 2/3 = 50

7 x 7 1/7 = 50

7.5 x 6 2/3 = 50

8 x 6 1/4 = 50

8.5 x 5 8/9 = 50

9 x 5 5/9 = 50

9.5 x 5 1/4 = 50

10 x 5     = 50

10.5 x 4 3/4 = 50

11 x 4 5/9 = 50

11.5 x 4 1/3 = 50

12 x 4 1/6 = 50

12.5 x 4     = 50

13 x 3 6/7 = 50

13.5 x 3 5/7 = 50

14 x 3 4/7 = 50

Will Mark Brainnlest Please help me​

Answers

Answer:

sory

Step-by-step explanation:

soryuuuiuuuiiiiiiijjjjkkkkkj

The answer is: 9m-n+6

Help fast pleaseeeeeeee

Answers

Step-by-step explanation:

-2. = [tex] \frac{1}{49} [/tex]-1 = [tex] \frac{1}{7} [/tex]0 = 11. = 72. = 49

There are 3200 students at Lake High School and 310 of these students are sophomores. If 38 of the sophomores are in favor of the school forming a crew team and 34 of the remaining students (not sophomores) are also in favor of forming a crew team, how many students are opposed to this idea?

Answers

Answer: 3128 students

Step-by-step explanation:

Total no of students in the school : 3200

No of sophomores in favor of the school forming a crew team : 38

No of the remaining students in favor of forming a crew team : 34

Total students in favor of forming a crew team = 38+34= 72

No of students against it : Total students - Students in favor

                                          = 3200-72 = 3128 students

Suppose AABC = AEFD, AEFD = AGIH, ZA = 90°, and mZF= 20°. What is mZH?
a. 20°
b. 70°
C. 90°
d. Cannot be determined

Answers

90+20= 110, a triangle is 180° so therefore, 180-110= 70. The answer is B!

8. What is the solution to 4(1/2x+7)=12?

Answers

Answer:

x=-8

Step-by-step explanation:

4(1/2x+7)=12

Divide each side by 4

4/4(1/2x+7)=12/4

(1/2x+7)=3

Subtract 7 from each side

1/2x+7-7=3-7

1/2x = -4

Multiply each side by 2

1/2x*2 = -4*2

x = -8

Answer:

-8

Step-by-step explanation:

Divide both sides by 4 which will give you 1/2x+7=3

Then multipy both sides by 2 which will then give you x+14=16

Then move the constant = x=6-14

6-14 is -8 which will give you x=-8

How would I answer this: How many minutes are in a 30-day month.... use vertical multiplication to get the right answer

Answers

Answer:

43,200 minutes in 1months or 30 days

There are 43200 minutes in one month.

What is multiplication?

The basic explanation of multiplication is adding a number, with respect to another number, repeatedly.

Given that, How many minutes are in a 30-day month,

We have, 60 minutes in 1 hour

And, 24 hours in 1 day,

Then, number of minutes in 1 day = 60 × 24 = 1440 minutes

Therefore, in 1 month = 1440 × 30 = 43200 minutes

Hence, there are 43200 minutes in one month.

Learn more about multiplication, click;

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A chef mix his salt and pepper. If he put 2/3 cup of salt and 1/2 cup of pepper in his shaker, what is the ratio of salt to pepper ?

Answers

Answer:

4 to 3

Step-by-step explanation:

The ratio of salt to pepper is

2/3 to 1/2

Multiply both fractions by 6

6 * 2/3 to 6 * 1/2

4 to 3

96 Children are on a school trip, there
are 7 seats in a mini bus. How many
mini bus are needed?

Answers

14 mini buses but there will be 1 seat open

Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why AABC= ALMN?
Check all that apply
O A. LL
O B. ASA
I C. LA
D. HL
E AAS

Answers

3 Answers:

Choice A.  LLChoice D.  HLChoice F.  SAS

==========================================================

Explanation:

Let's go through the answer choices one by one.

A) This can be used because LL = leg leg, and this means we have two pairs of congruent legs. Those pairs are AC = LN and CB = NM. The LL theorem only applies to right triangles.B) This cannot be used. We don't have info about two pairs of angles. We only know that one pair of angles are the same (those 90 degree angles). So we can't form the second "A" in "ASA". This idea will come up again in choice C and choice E.C) This cannot be used. Why not? Because the "A" of "LA" refers to "acute angle". But unfortunately we don't know anything about the acute angles (whether they are congruent or not). The LA theorem can only be applied to right triangles.D) This can be used. We can use the HL (hypotenuse leg) theorem because we see that AB = LM are the pair of congruent hypotenuses, and you can use any of the congruent leg pairs to form the L of HL. Similar to LL and LA, the HL theorem only works for right triangles.E) This cannot be used. Like with choice B, we can't form the second "A" of "AAS".F) This can be used because we have two pairs of congruent sides, with a pair of congruent angles between those sides. Those angles being the marked 90 degree angles. It turns out that LL theorem is a special case of the SAS theorem.

In short, we can use choice A, choice D, choice F. We can't use the other three choices because we lack the info about any other pairs of angles.

The congruence theorem or postulate that we can use to show that triangle ABC is congruent to triangle LMN is LL (Side-Side-Side), the correct option is A.

What are congruent triangles?

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]

(|AB| denotes length of line segment AB, and so on for others).

We are given that;

Sides are equal

Now,

Based only on the information given in the diagram, we can use the following congruence theorems or postulates to show that triangle ABC is congruent to triangle LMN:

A. LL (Side-Side-Side): This theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. In this case, we know that AB = LM, AC = LN, and BC = MN, so we can use LL to show that triangle ABC is congruent to triangle LMN.

B. ASA (Angle-Side-Angle): This theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. In this case, we do not know any angle measures, so we cannot use ASA to show that the triangles are congruent.

Therefore, by the  congruent triangles the answer will be LL (Side-Side-Side).

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