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Logarithm Evaluation and Simplification using Properties

Use properties of logarithms including quotient, product, and power properties to simplify and evaluate logarithmic expressions.

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Logarithm Evaluation and Simplification using Properties

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  1. Use 3 0.792 and 7 1.404to evaluate the logarithm. log log log log log log log log log 4 4 4 4 4 4 4 4 4 – 7 a. 3 = and and log log 3 3 Use the given values of Use the given values of – 0.792 1.404 log log 7. 7. 4 4 4 4 3 –0.612 = 7 Write 21 as 3 7. b. (3 7) 21 = 3 7 = + + 0.792 1.404 2.196 = EXAMPLE 1 Use properties of logarithms Quotient property Simplify. Product property Simplify.

  2. Use 3 0.792 and 7 1.404to evaluate the logarithm. log log log log log 4 4 4 4 4 c. 49 72 = Write 49 as 72 2 7 = log 7. 4 2(1.404) Use the given value of 2.808 = EXAMPLE 1 Use properties of logarithms Power property Simplify.

  3. Use 5 0.898 and 8 1.161 to evaluate the log log 6 6 logarithm. log log log log log log 6 6 6 6 6 6 – 8 log 1. 5 = 6 and Use the given values of and log log 5 5 Use the given values of – 0.898 1.161 log log 8. 8. 6 6 6 6 5 –0.263 = 8 Write 40 as 8 5. 2. (8 5) 40 = 8 5 = + + 1.161 0.898 2.059 = for Example 1 GUIDED PRACTICE Quotient property Simplify. Product property Simplify.

  4. Use 5 0.898 and 8 1.161 to evaluate the log log 6 6 logarithm. log log log log log log 6 6 6 6 6 6 3. 64 82 = Write 64 as 82 2 8 = log log 8. 5. 6 6 2(1.161) Use the given value of Use the given value of 2.322 = 4. 125 53 = Write 125 as 53 3 5 = 3(0.898) 2.694 = for Example 1 GUIDED PRACTICE Power property Simplify. Power property Simplify.

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