New Topic Exponents Exponential Equations I Exponential Functions The Exponential Function Base e The Logarithm Function Logarithmic & Exponential Equations Applications:Growth & Decay Review&Test

UNIT 5  : EXPONENTIAL & LOGARITHMIC FUNCTIONS

LESSON 1: LAWS OF EXPONENTS

Examples of Powers:

25 = 2 x 2 x 2 x 2 x 2 = 32;   (-3)3 = (-3) x (-3) x (-3) = -27;    2.72 = 2.7 x 2.7 = 7.29

A POWER  (am ) consists of two parts; the base “a” and the exponent “m”.

# Review of Basic Exponent Laws:

 Rule Example Explanation am x an = am+n 32 x 35 = 37 Multiplication Rule - If the bases are the same, add the exponents Division Rule - If the bases are the same, subtract the exponents (am)n = amn (32)3=36 Power Rule – When taking a power of a power, multiply the exponents (ab)m = amam (3 x 2)4 = 34 x 24 Power of a Product – Take each factor in the product to that power Power of a Quotient – Take numerator and denominator to that power

Example 1:  Simplify.

Solutions:

Example 2:  Simplify.

Solutions:

Example 3:  Simplify each of the following:

Solutions:

Alternate solution for c):

Rational Exponents:

Example 2:

Example 4:  Simplify

Solutions:

Example 5:  Simplify

Solutions:

Example 6:  Simplify

Solutions: