College Algebra Chapter 4 Exponential and Logarithmic Functions Section 4.4 Properties of Logarithms

1. Apply the Product, Quotient, and Power Properties of Logarithms 2. Write a Logarithmic Expression in Expanded Form 3. Write a Logarithmic Expression as a Single Logarithm 4. Apply the Change-of-Base Formula

Apply the Product, Quotient, and Power Properties of Logarithms Let b, x, and y be positive real numbers where b ≠ 1. Product Property: Quotient Property: Power Property: For these exercises, assume that all variable expressions represent positive real numbers.

Examples 1 – 3: Use the product property of logarithms to write the logarithm as a sum. Then simplify if possible. 1. 2. 3.

Examples 4 – 6: Use the quotient property of logarithms to write the logarithm as a difference. Then simplify if possible. 4. 5. 6.

Examples 7 – 9: Apply the power property of logarithms. 7. 8. 9.

1. Apply the Product, Quotient, and Power Properties of Logarithms 2. Write a Logarithmic Expression in Expanded Form 3. Write a Logarithmic Expression as a Single Logarithm 4. Apply the Change-of-Base Formula

Example 10: Write the expression as the sum or difference of logarithms.

Example 11: Write the expression as the sum or difference of logarithms.

Example 12: Write the expression as the sum or difference of logarithms.

Example 13: Write the expression as the sum or difference of logarithms.

Example 14: Write the expression as the sum or difference of logarithms.

Example 15: Write the expression as the sum or difference of logarithms.

1. Apply the Product, Quotient, and Power Properties of Logarithms 2. Write a Logarithmic Expression in Expanded Form 3. Write a Logarithmic Expression as a Single Logarithm 4. Apply the Change-of-Base Formula

Example 16: Write the logarithmic expression as a single logarithm with a coefficient of 1, and simplify as much as possible.

Example 17: Write the logarithmic expression as a single logarithm with a coefficient of 1, and simplify as much as possible.

Example 18: Write the logarithmic expression as a single logarithm with a coefficient of 1, and simplify as much as possible.

Example 19: Write the logarithmic expression as a single logarithm with a coefficient of 1, and simplify as much as possible.

Example 20: Write the logarithmic expression as a single logarithm with a coefficient of 1, and simplify as much as possible.

Examples 21 – 23: Use to approximate the value of 21. 22. 23.

1. Apply the Product, Quotient, and Power Properties of Logarithms 2. Write a Logarithmic Expression in Expanded Form 3. Write a Logarithmic Expression as a Single Logarithm 4. Apply the Change-of-Base Formula

Apply the Change-of-Base Formula Let a and b be positive real numbers such that a ≠ 1 and b ≠ 1. Then for any positive real number x In particular,

Examples 24, 25: Use the change-of-base formula and a calculator to approximate the logarithm to 4 decimal places. 24. 25.