Logarithm — Quiz 6

Questions in this quiz (6)

1. Find all real solutions of $$\log_3(x^2 - 2x - 3) = 2.$$

   • $$-4$$ or $$3$$
   • $$4$$ or $$3$$
   • $$4$$ or $$-3$$
   • $$-4$$ or $$-3$$

2. Given the equation $$\log_{3x}(4x^2+7)=2$$ and $$x$$ > $$0$$. What is the value of $$x$$?

   • $$\sqrt{\frac{3}{4}}$$
   • $$\sqrt{\frac{9}{5}}$$
   • $$\sqrt{\frac{7}{5}}$$
   • $$\sqrt{\frac{5}{2}}$$

3. If $$a$$, $$b$$, and $$c$$ are positive numbers such that $$a^x = b$$ and $$a^y = c$$, then what is $$xy$$?

   • $$\log_a (ac)$$
   • $$(\log_a b)+(\log_a c)$$
   • $$(\log_a b)(\log_a c)$$
   • $$(\log_a b)(\log_c b)$$

4. Solve for $$x$$ the equation $$\log\left(\log\left(2 + \log_2(x+1)\right)\right) = 0$$

   • 1
   • 10
   • 255
   • 256

5. Solve for $$x$$ in the equation $$3x \cdot a^{2\log_a x} = 432$$

   • $$144$$
   • $$\sqrt[3]{3}$$
   • $$\sqrt[3]{432}$$
   • $$\sqrt[3]{144}$$

6. Solve for $$x$$ in the equation:$$\ln(x+2) + \ln(3x-1) = 2\ln(x+3)$$

   • $$\frac{1 + \sqrt{89}}{4}$$
   • $$\frac{- \sqrt{89}}{4}$$
   • $$\frac{1 - \sqrt{89}}{2}$$
   • $$\frac{-1 - \sqrt{89}}{2}$$