An equation quadratic in e to the x, and single-term forms

The question

Name: ______________________   Date: ____________   An equation quadratic in e to the x, and single-term forms (6 points)

No calculator. Give exact values and show the work that leads to each answer.

1. (A(i)) Solve $e^{2x} - 3e^x - 10 = 0$ for $x$. [1 point]

2. (A(ii)) Explain why the other factor in part A(i) gives no solution. [1 point]

3. (B(i)) Rewrite $\frac{8^{x + 1}}{4^x}$ as a single power of $2$. [1 point]

4. (B(ii)) Rewrite $\ln(x^2 - 9) - \ln(x + 3)$ as a single natural logarithm with no fraction, for $x > 3$. [1 point]

5. (C) Solve $4^x - 6 \cdot 2^x + 8 = 0$ for $x$. [2 points]