Logarithmic Functions TS:Making Decisions After Reflection and Review

Objectives To write exponential equations in logarithmic form. To use properties of logarithms to expand and condense logarithmic expressions.

It is asking: “What power would I take b to in order to get a?” Logarithmic Functions Key to understanding logarithms: A logarithm is an exponent! Exponent Base Argument

Logarithmic Functions Exponential Form Logarithmic Form

Logarithmic Functions Evaluate:

Evaluate:

Evaluate:

Evaluate:

Evaluate:

Evaluate:

Evaluate:

Special Bases Common log Natural log

Natural Logarithm Evaluate:

Properties of Logarithms

Expand:

Expand: ln does not distribute!

Properties of Logarithms Expand:

Expand:

Conclusion A logarithm indicates the exponent to which you raise a certain base in order to produce a given value. The inverse of logarithmic function is an exponential function. Logs to the base 10 are written without a base. Logs to the base e are indicated by the symbol ln.

Begin your HW –Day 7 p.283 #1-8, Re-write the logarithmic equation as an exponential equation, or vise versa. 1)2)3)4)5)6)7)8) Apply the inverse properties of logarithmic and exponential functions to simplify. 23)24)25)26)27)28)

Logarithmic Functions Day 2 TS:Making Decisions After Reflection and Review

Objectives To use properties of logarithms to expand and condense logarithmic expressions. To be able to solve logarithmic and exponential equations

Properties of Logarithms

Combine:

Combine:

Combine:

Combine:

Combine:

Logarithmic Functions Solve:Solve:

Solve:Solve:

Solve:Solve:

Solve:Solve:

Suppose you deposit money into an account whose annual interest rate is 4% compounded continuously. How long will it take for the money to double?

Conclusion A logarithm indicates the exponent to which you raise a certain base in order to produce a given value. The inverse of logarithmic function is an exponential function. Logs to the base 10 are written without a base. Logs to the base e are indicated by the symbol ln.

Begin your HW –Day 8 p.284 #41-63,67, 71-77odd Write as a single logarithm. 41)42)43)44)45)46)47)48)49)50) Solve for x or t. 51)52)53)54)55)56)57)58)59)60)