Answer/Discussion on Logarithmic Properties

(Back to the tutorial on logarithmic properties)

College Algebra
Answer/Discussion to Practice Problems
on Logarithmic Properties

Answer/Discussion to 1a

What is the base in this problem?

This time the base is e. Make sure that you keep that same base throughout the problem.

*Use the product rule

*Use the definition of logs to simplify
*1/2 is the exponent needed on e to get e^1/2

(return to problem 1a)

Answer/Discussion to 1b

What is the base in this problem?

This time the base is 10. Make sure that you keep that same base throughout the problem.

*Use the quotient rule

*Use the definition of logs to simplify
*4 is the exponent needed on 10 to get 10000

(return to problem 1b)

Answer/Discussion to 1c

What is the base in this problem?

This time the base is 3. Make sure that you keep that same base throughout the problem.

*Use the product rule and the quotient rule

*Use the power rule

(return to problem 1c)

Answer/Discussion to 2a

What is the base in this problem?

This time the base is 10. Make sure that you keep that same base throughout the problem.

*Use the product rule

(return to problem 2a)

Answer/Discussion to 2b

What is the base in this problem?

This time the base is e. Make sure that you keep that same base throughout the problem.

*Use the power rule

*Use the quotient rule

(return to problem 2b)

Answer/Discussion to 3a

Note that the calculator can only evaluate logs that are base 10 or base e. Since this problem is in base 1.5, we need to change the base to base e (or base 10). Since the instructions say base e, let's do that.

*Use the change of base formula

*Use the calculator to find ln 20 and ln 1.5

*Divide

(return to problem 3a)

(Back to the tutorial on logarithmic properties)