To see the proofs of the product, quotient, and power laws of logarithms, read “Link the Ideas” on pages 394 to 395 of the textbook. Notice how each logarithmic law is proved using the exponent laws.

In Try This 2 you will look at using the laws of logarithms to evaluate an expression.

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Try This 2

Evaluate the expression using the laws of logarithms.

1. Write as a logarithm with no coefficient.
2. Write log6 18 − log6 2 as a single logarithm.
3. Use your answers from questions 1 and 2 to write the original expression as a single logarithm, and then simplify the expression.
4. Try to evaluate using your calculator. Can this be easily done on your calculator? If you did use your calculator, did you get the same answer?
   
   
   
   

   To enter logarithms into your calculator, use the LOG button. Some calculators let you enter the base of the logarithm using this button. For other calculators, the LOG button is the common logarithm with base 10. On these calculators, to enter log2 8, you need to use the change-of-base identity for logarithms. The identity states

   
   To write log2 8 as a logarithm of base 10, the expressions would become

    

   On your calculator you would enter LOG (8) ÷ LOG (2). Remember, when no base is indicated, it is assumed to be base 10.

Save your responses in your course folder.