Question

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

Answer 1

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

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

Answer 2

`\displaystyle x = (ln2)/(3)`

General Formulas and Concepts:

Pre-Algebra

• Equality Properties

Algebra II

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

Explanation:

Step 1: Define

Identify

`\displaystyle e^(3x) + 6 = 8`

Step 2: Solve for x

1. [Equality Property] Isolate x 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 x:
   `\displaystyle x = (ln2)/(3)`