Exponential and logarithmic functions Knowledge-Based Practice

Questions

1. 1.

   What is the solution set of the inequality $\log_{0.5}(3x - 1) \ge -3$?

   • A) $(-\infty, 3]$
   • B) $[3, \infty)$
   • C) $\left[\frac{1}{3}, 3\right]$
   • D) $\left(\frac{1}{3}, 3\right]$
2. 2.

   What is the inverse function $f^{-1}(x)$ of $f(x) = \log_5(2x - 3) + 4$ for $x > \frac{3}{2}$?

   • A) $f^{-1}(x) = \frac{5^{x+4} - 3}{2}$
   • B) $f^{-1}(x) = 2 \cdot 5^{x-4} + 3$
   • C) $f^{-1}(x) = \frac{5^{x-4} + 3}{2}$
   • D) $f^{-1}(x) = \frac{5^{x-4} - 3}{2}$
3. 3.

   What is the real solution to the equation $\log_4(x) + \log_{16}(x) + \log_{64}(x) = \frac{11}{6}$?

   • A) 2
   • B) 8
   • C) 16
   • D) 4
4. 4.

   What is the solution set of the equation $3^{2x+1} - 10 \cdot 3^x + 3 = 0$?

   • A) $\left\{\frac{1}{3}, 3\right\}$
   • B) $\{-1, 1\}$
   • C) $\{-3, 3\}$
   • D) $\{0, 1\}$
5. 5.

   What is the real solution to the equation $\log_2(x + 3) + \log_2(x - 1) = 5$?

   • A) $x = -7$ and $x = 5$
   • B) $x = 1$
   • C) $x = 5$
   • D) $x = 7$

Answers and step-by-step solutions appear after you finish the test.