5.5 Properties of Logarithms (1 of 3) Apply basic properties of logarithms Expand and combine logarithmic expressions Use the change of base formula

5.5 Properties of Logarithms (2 of 3) For positive numbers m, n, and a ≠ 1 and any real number r :

5.5 Properties of Logarithms (3 of 3) For positive numbers m, n, and a ≠ 1 and any real number r :

Expanding Versus Combining

Example: Expanding logarithmic expressions (1 of 3) Expand each expression. Write your answers without exponents.

Example: Expanding logarithmic expressions (2 of 3)

Example: Expanding logarithmic expressions (3 of 3)

Example: Combining terms in logarithmic expressions (1 of 6) Write each expression as the logarithm of a single expression.

Example: Combining terms in logarithmic expressions (2 of 6)

Example: Combining terms in logarithmic expressions (3 of 6) Write each expression as the logarithm of a single expression.

Example: Combining terms in logarithmic expressions (4 of 6)

Example: Combining terms in logarithmic expressions (5 of 6)

Example: Combining terms in logarithmic expressions (6 of 6)

Change of Base Formula Let x, a ≠ 1, and b ≠ 1 be positive real numbers. Then

Example: Applying the change of base formula (1 of 2) Use a calculator to approximate each expression to the nearest thousandth.

Example: Applying the change of base formula (2 of 2)

Example: Using the change of base formula for graphing Their graphs intersect near the point (3.104, 5). Solution is x ≈ 3.104.