1. Logarithmic Functions Categorized as Transcendental (Non-Algebraic) Functions Inverse of an Exponential Function Many real-life situations can be modeled using logarithmic functions, including: – Earthquake Intensity – Human Memory – Pace of life in Large Cities

2. Definition of Logarithmic Function

3. Examples Logarithmic FormExponential Form

4. Examples Logarithmic FormExponential Form 10 x = 100 10 to what exponent is 100? We call “10” the “common base” e x = 1 e to what exponent is 1? We call “e” the “natural base”

5. Properties of Logarithms

6. Xy=f(x) 1 2 4 8 Domain (0, ∞) Range (-∞, ∞) No y-intercept since y-axis is vertical asymptote x-intercept (1, 0) Continuous Neither even nor odd Increasing (0, ∞) No relative minimum or maximum Has an inverse (exponential)

7. Transformations learned in Chapter 1 still apply Parent is exponential function with base a Vertical translation –”d” Horizontal translation –”bx-c=0” Reflection on x-axis – “sign of a” Reflection on y-axis-”sign of b” Vertical Stretch or Shrink – “numeric value of a” EXAMPLES

8. Applications

9. The percentage of adult height attained by a girl who is x years old can be modeled by f(x) = 62 +35log (x -4) where x represents the girl’s age (from 5-15) and f(x) represents the percentage of her adult height. According to the model, what percentage of her adult height has a girl attained at age 13, rounded to nearest tenth?

10. Applications

11. Assignment Page 411 #53, 55, 59-63 odd, 113, 115, 119