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.
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. 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.
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