# Exponential and Logarithmic Functions

Topics: Natural logarithm, Logarithm, Derivative Pages: 4 (904 words) Published: February 6, 2011
EXPONENTIAL AND LOGARITHMIC FUNCTIONS

I.EXPONENTIAL FUNCTION
A. Definition
An exponential function is a function defined by f(x) = ax , where a > 0 and a ≠ 1. The domain of the function is the set of real numbers and the range is the set of positive numbers.

B. Evaluating Exponential Functions
1. Given: f(x) = 2x, find
a. f(3) = ____b. f(5) = _____c. f(-2) = ______ d. f(-4) = ______ 2. Evaluate f(x) = ( 1)x if
2
a. x = 2 ____b. x = 4 _____c. x = -3 ______ d. x = -4 _______

C. Graphing Exponential Functions
On the same Cartesian Coordinate plane, sketch the graphs of each set of exponential function 1. a) f(x) = 2xb. f(x) = 3xc. f(x) = 4x
2. a) f(x) = 2xb. f(x) = 2x + 1c. f(x) = 2x – 1
3. a) f(x) = 2xb. f(x) = 2x + 2c. f(x) = 2x – 3
4. a) g(x) = 2- xb. g(x) = 3- xc. g(x) = 4 – x

D. The Property of Equality for Exponential Equations
Let a, b and c be real numbers and a≠ 0, then ab = ac if and only if b = c Examples:
1. 32x = 362. 23x = 83. 643x = 84. 10- x = 1/10000
5. 43x = 16x + 26. 16- x = 1/647. 93x = [ 1/3]58.5x+2 – 5x + 1 + 5x = 2625

Do as directed:
A. Evaluate:
1. If f(x) = 3x, what is
a. f( 3)?= ____ b. f( 4) = _____c. f( -2) = _____ d. f( -4) = _____ 2. What is g(x) = [ 1/3 ]x if
a.x = 2 ____ b. x = 4 ______c. x = -3 ______ d. x = -4 ______

B. Solve for x
3. 2x = 1286. 243x = 3
4. 3x = 817. 2x + 2 + 2x + 1 + 2x = 896
5. 42x = 8x + 1 8. 272x – 2 = 95 – x

C. Challenge!!!
9. If x is real and x64 = 64, what is x32?
10. Find the value of xy if 2x = 7 and 7y = 64.
11. If 183 = 2x •3y, find the integer values of x and y. 12. There are about 1,000 bacteria in a certain culture. If the amount doubles every 2 Hours, about how many bacteria would there be after 8 hours?

13. A radioactive substance is decaying (it is changing into...