Courses   <-  Sean Forman   <-  You Are Here Properties of Logarithms

MAT 1151, Business Math, Sean Forman

Fall 2002

Work out the following by hand. This is to get you comfortable using the log rules.

Suppose $\ln 5=a$ and $\ln 2=b$.

1. For example, $\ln 10 = \ln (5 \times 2) = \ln 5 + \ln 2 = a + b$

2. $\ln 2/5$

3. $\ln 2.5$

4. $\ln 25$

5. $\ln \sqrt[4]{40}$

6. $\ln 5e^3$

Write the following as a sum or difference of logarithms.

1. $\ln (x^4\sqrt{x^2 + 1})$

2. $\log (\frac{x^3}{x^2 - 1})$

3. $\ln [ \frac{\sqrt[3]{x^2 + 2x + 1}}{x^2 - 1} ]^\frac{2}{3}$

Write the following as a single logarithm.

1. $\log u^2 - \log v$

2. $\log (\frac{1}{x^2} ) +\log (\frac{1}{x} )$

3. $21 \log \sqrt[3]{x} + \log 9x^2 - \log 25$

Find the exact value of the following expressions

1. $10^{\log 5 - \log 6}$

2. $e^{\ln 2 + 2 \ln 4}$

Given the following interest rates, determine how long it would take a dollar to (a) double, (b) triple.

1. 13%

2. 2.4%