RULES OF LOGARITHMS - Problem 5

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: .

Problem 5: Simplify tex2html_wrap_inline164 and calculate the value.

Answer: - 3.487

Solution : There are many ways to work the above problem. We have included two of the ways.

Solution 1:

Step 1: First note that you are taking the log of an expression raised to a power; therefore, you use Rule 3. tex2html_wrap_inline164

can be written tex2html_wrap_inline168

Step 2: You will now be taking the log of a quotient; therefore, use Rule 2.

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Step 3: You will now be taking logs of products; therefore, use Rule 1.

Step 4: You will now be taking logs of expressions raised to a power, use Rule 3.

Step 5: This last expression can be written

rounded to 3.487.

Step 6: You can check your answer by calculating directly from the initial expression.

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Since both answers are the same, you have correctly worked the problem.

Solution 2:

Step 1: First note that you are taking the log of an expression raised to a power; therefore, you use Rule 3.

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Step 2: Simplify the numerator and simplify the denominator: tex2html_wrap_inline168

can be written

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Step 3: Calculate the logarithm:

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