Suggested Practice on Moodle Worksheet: Logarithms Problems Logarithms & Laws of Logs Exponents and Logs 3 People have 10 fingers and 10 toes. It makes sense to use base 10. Natural-e Suggested Practice on Moodle Worksheet: Logarithms Problems

What is a logarithm? A logarithm is simply a way of solving for the exponent in an exponential equation. An exponential equation can be converted to a logarithmic equation as follows – and the process can be reversed to convert a logarithmic equation into an exponential equation. Where ‘x’ is the logarithm and ‘a’ is the base. *Read as “x is the logarithm of y to base a” Examples: Convert to exponential form: Convert to logarithmic form:

Evaluating Logarithms To solve a logarithmic expression, such as think: “to what power must I raise_____ to get ______? Examples: Some special cases (and the resulting general rules) Examples: General Rule: *Note: is undefined, and is undefined if

Special Base ‘e’ & Calculating Logs The base in a logarithm can be any real number, but if the base is ‘e’ then a special notation is used: will be written as Calculating the following logarithms with a calculator: Special Properties:

Properties (Laws) of Logarithms Logarithm of a Product: 1. Write the following as single logarithms 2. Given that and , evaluate the following: 3. Solve the following logarithmic equation:

Laws of Logarithms – cont’d Logarithm of a Quotient: 4. Write the following as single logarithms: 5. Solve the following logarithmic equation:

Laws of Logarithms – cont’d Logarithm of a power: 6. Given that and , evaluate: Change of base: 7. Calculate the following by changing to log2:

Practice Questions: Equality Property of Logarithms *IB Exam Style Question Equality Property of Logarithms Solve the following logarithmic equations