### 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

#1:

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

$$a)\hspace{.2em}\text{log}_{7}(-6)$$

$$b)\hspace{.2em}\text{log}_{2}(6)$$

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#2:

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

$$a)\hspace{.2em}\text{log}_{6}(65)$$

$$b)\hspace{.2em}\text{log}_{7}(47)$$

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#3:

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

$$a)\hspace{.2em}\text{log}_{2}(49)$$

$$b)\hspace{.2em}\text{log}_{3}(1)$$

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#4:

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

$$a)\hspace{.2em}\text{log}_{3}(2.2)$$

$$b)\hspace{.2em}\text{log}_{3}(16)$$

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#5:

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

$$a)\hspace{.2em}\text{log}_{5}(-25)$$

$$b)\hspace{.2em}\text{log}_{2}(25)$$

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Written Solutions:

#1:

Solutions:

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

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

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#2:

Solutions:

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

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

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#3:

Solutions:

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

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

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#4:

Solutions:

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

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

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#5:

Solutions:

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

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