160 likes | 175 Views
Chapter 5 Exponential and Logarithmic Functions. Properties of Logarithms. 5.5. Apply basic properties of logarithms Expand and combine logarithmic expressions Use the change of base formula. Properties of the Logarithm.
E N D
Chapter 5 Exponential and Logarithmic Functions
Properties of Logarithms 5.5 Apply basic properties of logarithms Expand and combine logarithmic expressions Use the change of base formula
Properties of the Logarithm For positive numbers m, n, and a ≠ 1 and any real number r :
Expand each expression. Write your answers without exponents. Solution Example: Expanding logarithmic expressions
Write each expression as the logarithm of a single expression. Example: Combining terms in logarithmic expressions
Write each expression as the logarithm of a single expression. Example: Combining terms in logarithmic expressions
Change of Base Formula Let x, a ≠ 1, and b ≠ 1 be positive real numbers. Then
Use a calculator to approximate each expression to the nearest thousandth. Solution Example: Applying the change of base formula Slide 5.5 - 14
Solve the equation graphically. Solution Graph Y1 = log(X^3 + X – 1)/log(2) and Y2 = 5. Their graphs intersect near the point (3.104, 5). Solution is x ≈ 3.104. Example: Using the change of base formula for graphing