# 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 and calculate the value.

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. can be written .
Step 2: You will now be taking the log of a quotient; therefore, use Rule 2. 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. 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. Step 2: Simplify the numerator and simplify the denominator: can be written Step 3: Calculate the logarithm: If you want to work another problem, click on Next Problem. [Previous Problem] [Next Problem] [Menu Back to Rule 3]

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