Logarithmic Functions
Objectives To write exponential equations in logarithmic form. To use properties of logarithms to expand condense logarithmic expressions. Don’t be afraid of logs!
Logarithmic Functions Key to understanding logarithms: A logarithm is an exponent! Exponent Base Argument
Logarithmic Functions Exponential Form Logarithmic Form
Logarithmic Functions Evaluate:
Logarithmic Functions Evaluate:
Logarithmic Functions Evaluate:
Logarithmic Functions Evaluate:
Logarithmic Functions Evaluate:
Logarithmic Functions Evaluate:
Logarithmic Functions Evaluate:
Special Bases Common log Natural log
Natural Logarithm Evaluate:
Properties of Logarithms
Properties of Logarithms Expand:
Properties of Logarithms Expand: ln does not distribute!
Properties of Logarithms Expand:
Properties of Logarithms Expand:
Properties of Logarithms Combine:
Properties of Logarithms Combine:
Properties of Logarithms Combine:
Properties of Logarithms Combine:
Properties of Logarithms Combine:
Solving Equations Using Logs Solve:
Solving Equations Using Logs Solve:
Solving Equations Using Logs Solve:
Solving Equations Using Logs Solve:
Using Logarithms 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?
Using Logarithms Chris wants to buy a car. It costs $30, 000, and he only has $27, 000. If he invests it in a bank account at 6% interest compounded quarterly, how long will he have to wait before it matures to $30, 000?
Logarithmic Functions Consider:
Logarithmic Functions
Logarithmic Functions The inverse of a logarithmic function is an exponential function.
Logarithmic Functions (red)
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.
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