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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}
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