RULES OF LOGARITHMS - Rule 2

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 2: tex2html_wrap_inline275

Example 1: Suppose that a base is 6 and exponents are 10 and 3. We could solve the exponential problem tex2html_wrap_inline277 by calculating tex2html_wrap_inline279 and

tex2html_wrap_inline281 and dividing the results. tex2html_wrap_inline283 , tex2html_wrap_inline285 and their quotient is tex2html_wrap_inline287 . You could also solve the problem by first combining the exponents

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The same is true of logarithms. Suppose you wanted to calculate

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You could calculate the answer by first dividing 60,466,176 by 216, changing the base of 6 to either 10 or e and calculating the results.

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Or you could first combine the logarithms using Rule 2 and then change the bases.

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Example 2: Calculate tex2html_wrap_inline297 .

Solution: Note that

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Using Rule 2 you could also work the problem by separating tex2html_wrap_inline297 .

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

Work the following problems. If you would like to review the answers and solutions, click on answer.

Problem 1: Calculate tex2html_wrap_inline305 .

Answer

Problem 2: Calculate tex2html_wrap_inline307 .

Answer

Problem 3: Calculate tex2html_wrap_inline309 .

Answer

Problem 4: Calculate tex2html_wrap_inline311 .

Answer

Problem 5: Simplify tex2html_wrap_inline313 and write the answer in terms of a base 10. What assumptions must be made about a, b, d, and d before you can work this problem?

Answer

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Author: Nancy Marcus

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