Exponential and logarithmic functions Knowledge-Based Download PDF

Questions

1. 1.

   Which expression represents the inverse function $f^{-1}(x)$ of $f(x) = \ln\left(\frac{x + 2}{x - 3}\right)$ defined for $x > 3$?

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

   What is the real solution to the equation $\frac{e^x - e^{-x}}{e^x + e^{-x}} = \frac{1}{3}$?

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

   What is the real solution to the equation $\log_2(x) + \log_4(x) + \log_8(x) = 11$?

   • A) $x = 32$
   • B) $x = 64$
   • C) $x = 128$
   • D) $x = 256$
4. 4.

   What is the real solution to the equation $4^x - 5 \cdot 2^x - 24 = 0$?

   • A) $x = 8$
   • B) $x = 3$
   • C) $x = -3$
   • D) $x = \log_2(24)$
5. 5.

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

   • A) $x = 5$
   • B) $x = 5$ and $x = -7$
   • C) $x = 7$
   • D) $x = 3$