RULES OF LOGARITHMS - RULE 3

Let a be a positive number such that a does not equal 1, let n be a real number, and let u and v be positive real numbers.

Logarithmic Rule 3: tex2html_wrap_inline121 .

Example 1: Find tex2html_wrap_inline123 two ways.

Solution: Since tex2html_wrap_inline125 can be written tex2html_wrap_inline127 , the expression tex2html_wrap_inline123 can be written

displaymath131

which in turn can be written

displaymath133

We have

displaymath135

and

displaymath137


Example 2: Find tex2html_wrap_inline139 .

Solution: The expression tex2html_wrap_inline139 can be written tex2html_wrap_inline143 which in turn can be written tex2html_wrap_inline145 . This last expression can be rewritten using Rule 1 as

displaymath147

This represents 6 identical terms and we can write the sum of the six terms as tex2html_wrap_inline149 .

Check: The original expression tex2html_wrap_inline139 can be written

displaymath153

The last expression tex2html_wrap_inline149 can be written

displaymath157


If you would like to review another example, click on Example.

Work the following problems and if you want to check your answer, click on answer.

Problem 1: Find tex2html_wrap_inline159

Answer

Problem 2: Find tex2html_wrap_inline161

Answer

Problem 3: Simplify tex2html_wrap_inline163

Answer

Problem 4: Simplify tex2html_wrap_inline165

Answer

Problem 5: Simplify tex2html_wrap_inline167

Answer

Problem 6: Simplify tex2html_wrap_inline169 . What assumptions must you make before you can begin work on this problem?

Answer

Problem 7: Simplify the following term completely

displaymath171

State the domain that makes your final answer equal to the original expression.

Answer

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Author: Nancy Marcus

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