Logarithm — Quiz 5

Questions in this quiz (6)

1. Which of these is equivalent to $$\log_a(c) \cdot \log_c(a)$$?

   • $$c^a$$
   • $$ac$$
   • $$a - c$$
   • $$1$$

2. Find the value of $$\log_{16} \left( \frac{1}{4} \right)^{5/4}.$$

   • $$\frac{5}{4}$$
   • $$-\frac{5}{16}$$
   • $$-\frac{5}{4}$$
   • $$-\frac{5}{8}$$

3. Express $$\log_x \left( \frac{y^m}{z^n} \right)$$ in terms of natural logarithms.

   • $$\frac{n \ln(y) + m \ln(z)}{\ln(x)}$$
   • $$\frac{n \ln(x) - m^2 \ln(z)}{\ln(y)}$$
   • $$\frac{m \ln(y) - n \ln(z)}{ln(x)}$$
   • $$\frac{n \ln(v) - m \ln(x)}{\ln(y)}$$

4. If $$\log_5 2 = p$$ and $$\log_5 3 = q$$, which of the following is equal to 18?

   • $$5^{3q + p}$$
   • $$5^{2q + 3p}$$
   • $$5^{q + 2p}$$
   • $$5^{2q - p}$$

5. If $$\log 3 = p$$ and $$\log 7 = q$$, express $$\log 63$$ in terms of $$p$$ and $$q$$.

   • $$2p - q$$
   • $$p + 2q$$
   • $$2p + 2q$$
   • $$2p + q$$

6. What is the $$x$$-coordinate of the intersection point of $$y = \log(x + 5) + 3$$ and $$y = 6$$ in the standard xy-coordinate plane?

   • $$-5$$
   • $$6$$
   • $$995$$
   • $$1000$$