Question

what is the value of (x) if (e^{3x+6} = 8)?

• (x = \frac{\ln 8 - 6}{3})
• (x = \frac{\ln 6 - 8}{3})
• (x = \frac{\ln 8 + 6}{3})
• (x = \frac{\ln 6 + 8}{3})

Explanation:

Take the natural logarithm of both sides

Using the Solving Exponential Equations Algebraically knowledge point

$$
LATEXBLOCK0
$$

Isolate the variable term

Using the Solving Exponential Equations Algebraically knowledge point

$$ 3x = \ln(8) - 6 $$

Solve for x

Using the Solving Exponential Equations Algebraically knowledge point

$$ x = \frac{\ln(8) - 6}{3} $$

Answer:

• (A) \(x = \frac{\ln 8 - 6}{3}\) (Correct answer)
• (B) \(x = \frac{\ln 6 - 8}{3}\)
• (C) \(x = \frac{\ln 8 + 6}{3}\)
• (D) \(x = \frac{\ln 6 + 8}{3}\)