3.3 Day 1 Properties of logarithms –Use the product rule. –Use the quotient rule. –Use the power rule. –Expand logarithmic expressions. Pg. 407 # 2-36 even

Product Rule: When multiplying quantities with a common base, we add exponents. When we find the logarithm of a product, we add the logarithms Example: Logarithms are Exponential Expressions Rules for logarithms come from rules for exponents

Use the product rule to expand each logarithmic expression: 1. log 6 (7. 11) 2. log(100x) Product Rule:

Quotient Rule: When dividing expressions with a common base, we subtract exponents, thus we have the rule for logarithmic functions: Example:

Use the quotient rule to expand each logarithmic expression: Quotient Rule:

Power Rule: When you raise one exponent to another exponent, you multiply exponents. Thus, when you have a logarithm that is raised to a power, you multiply the logarithm and the exponent (the exponent becomes a multiplier) Example: Simplify

Use the power rule to expand each logarithmic expression: Power Rule:

Expanding Logarithmic Expressions Use properties of logarithms to change one logarithm into a sum or difference of others. Example

Use logarithmic properties to expand each expression as much as possible: 8. 9.