LOGARITHMIC AND EXPONENTIAL EQUATIONS Intro to logarithms and solving exponential equations.

Solving Logarithmic Equations Type 1: log = number Isolate log Change to exponential form Solve for x CHECK FOR EXTRANEOUS SOLUTIONS! (cannot take the log of a negative number)

Solving Logarithmic Equations

Properties of Logarithms Product Property Quotient Property Power Property = = =

Expanding and Condensing Logarithms Expanding Use the properties of logarithms to change a single logarithm into multiple logarithms with the same base Condensing Use the properties of logarithms to combine multiple logarithms with the same base into one single logarithm

Examples

Solving Equations by Condensing the Logarithm Type 3: multiple logs on either side Condense one or both sides of the equation Then solve the logarithmic equation using previous methods Log=number: change to exponential form and solve Log=log: cancel out logs and solve

Examples

Exponential Equations Equations that have a variable in the exponent Type 1: Numeric base Isolate the exponential term Change to logarithmic form Solve for the variable Use the change of base formula to type into calculator Round solutions to three decimal places if necessary

Exponential Equations Type 2: Base e Isolate the exponential term Take ln of both sides Cancel out ln and e Solve the remaining equation and evaluate using calculator Round solutions to three decimal places if necessary

Examples