Question

which of the following is the solution of (5e^{2x} - 4 = 11)?

• (x = \ln 3)
• (x = \ln 27)
• (x = \frac{\ln 3}{2})
• (x = \frac{3}{\ln 3})

Explanation:

Isolate the exponential term

Using the Solving Exponential Equations Algebraically knowledge point

$$
LATEXBLOCK0
$$

Apply the natural logarithm

Using the Inverse Properties of Logarithms knowledge point

$$
LATEXBLOCK1
$$

Solve for x

Using the Solving Exponential Equations Algebraically knowledge point

$$ x = \frac{\ln(3)}{2} $$

Answer:

• (A) \(x = \ln 3\)
• (B) \(x = \ln 27\)
• (C) \(x = \frac{\ln 3}{2}\) (Correct answer)
• (D) \(x = \frac{3}{\ln 3}\)