1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Zepler [3.9K]
3 years ago
5

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

Mathematics
2 answers:
geniusboy [140]3 years ago
8 0

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

charle [14.2K]3 years ago
3 0

Answer:

\displaystyle x = \frac{ln2}{3}

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Equality Properties

<u>Algebra II</u>

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

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle e^{3x} + 6 = 8

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. [Equality Property] Isolate <em>x</em> term:                                                                   \displaystyle e^{3x} = 2
  2. [Equality Property] ln both sides:                                                                    \displaystyle lne^{3x} = ln2
  3. Rewrite [Logarithmic Property - Exponential]:                                                \displaystyle 3xlne = ln2
  4. Simplify:                                                                                                             \displaystyle 3x = ln2
  5. [Equality Property] Isolate <em>x</em>:                                                                            \displaystyle x = \frac{ln2}{3}
You might be interested in
3 more than 3 times a number is equal to 12 less than 6 times the number. what is the number?
lorasvet [3.4K]

Answer:

Step-by-step explanation:

18

5 0
3 years ago
Read 2 more answers
Determine the IQR for this set of data. 12, 13, 14, 15, 17, 18, 19, 19, 22, 23<br> 14 <br> 17.5
VladimirAG [237]

Answer:5

Step-by-step explanation:

4 0
3 years ago
What is the circumference of a circle with a<br> diameter of 3 cm? (Use 3.14 as pi)
hoa [83]

Answer:

circumference=9.42

Step-by-step explanation:

the formula for circumference is pi x diameter.

4 0
3 years ago
Why are whole numbers rational numbers? Use 15 as an example.
svlad2 [7]

Answer:

Every whole number n can be written as a fraction of integers.

Step-by-step explanation:

Every whole number n can be written as a fraction of integers: x=x/1.

If we use 15 as an example, it would be 15 = 15/1. 15/1 is 15.

So whole numbers are rational

5 0
3 years ago
Read 2 more answers
What is the LCD of , 3/4 ,4/5 and 7/10
lesantik [10]

Answer:

20

Step-by-step explanation:

20 is divisible by 4, 5 and 10

4 0
3 years ago
Other questions:
  • Need help with a math question PLEASE HELP
    6·1 answer
  • A family has two cars. the first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of
    14·1 answer
  • Is r2+8r+16=0 lenear equation or not​
    6·1 answer
  • I need help! Please. Justify answer using Intermediate value theorem (IVT)
    7·1 answer
  • What is the approximate length of the hypotenuse of a right triangle with vertices (-6, 2),
    9·1 answer
  • Which expression represents a number that is one fourth as great as 10-2?
    11·1 answer
  • 5) Tess deposited $500 in an account that earns 6% annual simple interest. She leaves the money in the account for 4 years. What
    14·1 answer
  • HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
    7·1 answer
  • Math is hard plz help
    11·2 answers
  • Lf f(x) = -4x^2- 6x-1 and g(x) = -x^2 - 5x + 3, find (f- g)(x)
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!