### About Change of Base Formula:

We can use the change of base rule to change the base of a logarithm into one that is more convenient to work with. We can use this method to obtain a common logarithm or natural logarithm. These two types of logarithms appear on most calculators and can be used to obtain a decimal approximation.

Test Objectives
• Demonstrate the ability to approximate the value of a common logarithm
• Demonstrate the ability to approximate the value of a natural logarithm
• Demonstrate the ability to use the change of base rule to generate a common or natural logarithm
Change of Base Formula Practice Test:

#1:

Instructions: approximate each (round to the nearest thousandth).

$$a)\hspace{.2em}log_{7}(-6)$$

$$b)\hspace{.2em}log_{2}(6)$$

#2:

Instructions: approximate each (round to the nearest thousandth).

$$a)\hspace{.2em}log_{6}(65)$$

$$b)\hspace{.2em}log_{7}(47)$$

#3:

Instructions: approximate each (round to the nearest thousandth).

$$a)\hspace{.2em}log_{2}(49)$$

$$b)\hspace{.2em}log_{3}(1)$$

#4:

Instructions: approximate each (round to the nearest thousandth).

$$a)\hspace{.2em}log_{3}(2.2)$$

$$b)\hspace{.2em}log_{3}(16)$$

#5:

Instructions: approximate each (round to the nearest thousandth).

$$a)\hspace{.2em}log_{5}(-25)$$

$$b)\hspace{.2em}log_{2}(25)$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}Undefined$$

$$b)\hspace{.2em}2.585$$

#2:

Solutions:

$$a)\hspace{.2em}2.33$$

$$b)\hspace{.2em}1.979$$

#3:

Solutions:

$$a)\hspace{.2em}5.615$$

$$b)\hspace{.2em}0$$

#4:

Solutions:

$$a)\hspace{.2em}0.718$$

$$b)\hspace{.2em}2.524$$

#5:

Solutions:

$$a)\hspace{.2em}Undefined$$

$$b)\hspace{.2em}4.644$$