Logarithm — Quiz 3

Questions in this quiz (6)

1. If $$\log_b(x \cdot y^2) = z$$, what is $$y$$ in terms of the other variables?

   • $$\sqrt{\frac{b}{x}}$$
   • $$\sqrt{\frac{b^z}{z}}$$
   • $$b^{\frac{z - \log_b(x)}{2}}$$
   • $$\frac{b^z}{x}$$

2. Find the approximate value of $$\log_6(2) + \log_2(6).$$

   • 1
   • 0
   • 1.93
   • 2.97

3. Find the simplified value of $$\log_3\left(27^{5/2}\right)$$.

   • $$\frac{15}{2}$$
   • $$\frac{10}{3}$$
   • $$\frac{5}{3}$$
   • $$\frac{25}{6}$$

4. Find the value of $$\log_3\left(\sqrt[4]{9} \cdot \sqrt[3]{27}\right).$$

   • $$\frac{7}{4}$$
   • $$\frac{3}{2}$$
   • $$\frac{5}{3}$$
   • $$\frac{13}{4}$$

5. Find the value of $$\log_b\left(\frac{b^6}{\left(\sqrt[3]{b}\right)^4}\right).$$

   • $$\frac{14}{3}$$
   • $$\frac{3}{7}$$
   • $$\frac{6}{7}$$
   • $$\frac{15}{7}$$

6. Find the simplified value of $$\log \left( \frac{10^{3a}}{100^{2b}} \right).$$

   • $$2a - 3b$$
   • $$3a - 2b$$
   • $$a - 3b$$
   • $$3a - 4b$$