1.7 Rational exponents, laws of logarithms and exponential equations Quiz

1. Find $8^{\frac{2}{3}}$.

• A. $\frac{16}{3}$
• B. $4$
• C. $2$
• D. $64$

2. Simplify $\log_5 50 - \log_5 2$.

• A. $2$
• B. $\log_5 48$
• C. $25$
• D. $\log_5 100$

3. Express $\log_9 x$ in terms of $\log_3 x$.

• A. $2\log_3 x$
• B. $\frac{1}{2}\log_3 x$
• C. $\log_3 x - 2$
• D. $(\log_3 x)^2$

4. Solve $\left(\frac13\right)^x = 9^{x+1}$.

• A. $x = -\frac{2}{3}$
• B. $x = -2$
• C. $x = \frac{2}{3}$
• D. $x = -1$

5. Solve $2^{x-1} = 10$.

• A. $x = 6$
• B. $x = \log_2 10 - 1$
• C. $x = 1 + \log_2 10$
• D. $x = \frac{10}{2}+1$