3.3 Properties of Logarithms
There are several properties of logarithms which make it easier for us to deal with logarithmic equations. These properties are related to some common properties of exponents.
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Use one or more of the properties above to expand each logarithmic expression below. Simplify when possible.
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The last few examples have illustrated the process of expanding a logarithmic expression. To condense a logarithmic expression, we use the properties in the other order, i.e. write a sum of logs as the log of a product, the difference of logs as the log of a quotient, and the multiple of a log as the log raised to a power.
Use the properties to condense each logarithmic expression below.
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Given that logb2 = A and logb3 = C, find each of the following:
a) logb(8)
b) logb(2/9)
c) logb( 3)
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We know how to evaluate certain logarithms that have nice answers, and we can evaluate any common or natural logarithm with a calculator, but suppose we are asked to evaluate a logarithm such as the following:
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We can even use the change­of­base property to graph logarithmic functions with other bases.
Ex. Graph each function below with your calculator by using the change­of­base property.
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