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:
$$a)\hspace{.2em}\text{Undefined}$$
$$b)\hspace{.2em}4.644$$
