In Check it Out, you uncovered the three laws of logarithms. The following textbook examples show you how these laws can be used.
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Read pages 443-445 Examples 1, 2 and 3 in your textbook, Principles of Mathematics 12. Complete the Your Turn questions on page 444 (top and bottom of page) and page 445 for more practice using the laws of logarithms. Click here to verify your answers. |
In Lesson 7A, you learned that the graphs of logarithmic functions and exponential functions are inverses. Compare the operations used in each logarithm law to its corresponding exponent law. The operations are also inverses. This knowledge gives a different perspective on the laws of logarithms, which can be helpful when solving problems.
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Laws of Exponents
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Laws of Logarithms
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When you multiply powers with the same base, the resulting power has the same base and the exponent is obtained by adding the original exponents.
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When you add logarithms with the same base, the resulting logarithm has the same base and the argument is obtained by multiplying the original arguments.
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Laws of Exponents
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Laws of Logarithms
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When you divide powers with the same base, the resulting power has the same base and the exponent is obtained by subtracting the original exponents.
Examples:
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When you subtract logarithms with the same base, the resulting logarithm has the same base and the argument is obtained by dividing the original arguments. Examples:
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Laws of Exponents
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Laws of Logarithms
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When a power is being raised to an exponent, the resulting power has the same base and the exponent is obtained by multiplying the original exponents.
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When a logarithm is multiplied by a value (constant or variable), the resulting logarithm has the same base and the argument is raised to an exponent equal to that constant or variable.
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One final tool that you can use when simplifying logarithmic expressions is the change of base formula. Use this to evaluate a logarithm that is not base 10 or e.
