Exponential and logarithmic equations and a single logarithm

The question

Name: ______________________   Date: ____________   Exponential and logarithmic equations and a single logarithm (6 points)

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

1. (A(i)) Solve $2e^{3x - 1} + 5 = 19$ for $x$. [1 point]

2. (A(ii)) Solve $\log_2 x + \log_2(x + 6)$$= 4$ for $x$. [1 point]

3. (B(i)) Rewrite $2\ln(x + 1) - \ln x + 3\ln 2$ as a single natural logarithm, for $x > 0$. [1 point]

4. (B(ii)) Rewrite $9^x \cdot 3^{2 - x}$ as a single power of $3$. [1 point]

5. (C) Solve $3 - \log_2(x + 1) \ge 1$ for $x$. [2 points]