Exponential and Logarithmic Functions — Quiz 3

Questions in this quiz (9)

1. If $$\log a=3$$ and $$\log b=1$$, what is the numerical value of $$\log\left(\frac{a^2}{\sqrt{b}}\right)$$?

   • $$4.5$$
   • $$5.0$$
   • $$5.5$$
   • $$6.0$$

2. The expression $$2\log x-\frac{1}{2}\log y$$ is equivalent to which expression?

   • $$\log\left(\frac{x^2}{\sqrt{y}}\right)$$
   • $$\log\left(\frac{x^2}{y^{2}}\right)$$
   • $$\log(x^2y)$$
   • $$\log\left(\frac{\sqrt{x}}{y}\right)$$

3. If $$\log N=\frac{1}{2}(\log a+\log b)-\log c$$, what does $$N$$ equal?

   • $$\frac{\sqrt{ab}}{c}$$
   • $$\frac{ab}{c^2}$$
   • $$\frac{a+b}{c}$$
   • $$\frac{\sqrt{a}+\sqrt{b}}{c}$$

4. If $$f(x)=\log(x^3)$$ and $$g(x)=\frac{x}{100}$$, then $$f(g(x))$$ equals which expression?

   • $$3(\log x-2)$$
   • $$\log\left(\frac{x^3}{100}\right)$$
   • $$3\log x+2$$
   • $$\frac{3\log x}{100}$$

5. What is the domain of the graph of $$f(x)=\log(x-3)$$?

   • $$(0,\infty)$$
   • $$(3,\infty)$$
   • $$( -\infty,3)$$
   • $$( -\infty,\infty)$$

6. If $$\log 50=b$$, which expression is equivalent to $$(b-1)$$?

   • $$\log 5$$
   • $$\log 49$$
   • $$\log 500$$
   • $$2\log 5$$

7. If $$\log_2(x^2+3)=3$$, what is the value of $$x$$?

   • $$-\sqrt{5},\sqrt{5}$$
   • $$\sqrt{5}$$
   • $$-\sqrt{5}$$
   • No solution

8. Which function is the inverse of $$y=\log(x-2)$$?

   • $$y=10^x-2$$
   • $$y=10^x+2$$
   • $$y=2^x-2$$
   • $$y=\left(\frac{1}{10}\right)^x-2$$

9. A company tracked the number of downloads of their app for the first 12 days after launch. The data are shown below. The company noticed that the growth rate slowed over time and wants to model the data to predict future downloads. Which regression equation best models the data?

   • $$y=210.4+380.2\ln(x)$$
   • $$y=350.1+210.3\ln(x)$$
   • $$y=180.2+450.6\ln(x)$$
   • $$y=420.5+180.7\ln(x)$$