Question

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

Answer 1

Answer:

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

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

Step-by-step 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:                                                                            $\displaystyle x = \frac{ln2}{3}$

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