Logarithm — Quiz 2

Questions in this quiz (5)

1. Find the constant $$B$$ such that $$\log_2 x = B\log_{10} x$$ for all $$x$$ > $$0$$.

   • $$\frac{1}{\log_{2} 10}$$
   • $$\frac{1}{\log_{10} 2}$$
   • $$\frac{-1}{\log_{2} 10}$$
   • $$\frac{-2}{\log_{2} 10}$$

2. Express $$(\log x)(\log_b a)$$ as a single logarithm.

   • $$\log_b(\log a)$$
   • $$\log_b(-\log a)$$
   • $$\log_b(x^{\log a})$$
   • $$\log_a(\log b)$$

3. Find $$a$$ so that the graph of $$y = \log_a x$$ passes through the point $$(e, 2)$$.

   • $$\sqrt{2}$$
   • $$\sqrt{x}$$
   • $$e$$
   • $$\sqrt{e}$$

4. Given: $$\log_8(5) = b$$. Express $$\log_4(10)$$ in terms of $$b$$.

   • $$\frac{2b}{3}$$
   • $$\frac{b}{2}$$
   • $$\frac{5b}{8}$$
   • $$\frac{1 + 3b}{2}$$

5. Simplify: $$\log_3(243) + \left[\log(50) - \log(5)\right] \div \log(25)$$

   • $$5 + \frac{1}{2\log(5)}$$
   • $$\frac{1}{2\log(243)}$$
   • $$-\frac{1}{5\log(243)}$$
   • $$\frac{1}{\log(243)}$$