1. 4.3 – Logarithmic functions
Target Goals:
Use the relationship between exponential and logarithmic functions to change them into the opposite form
Evaluate logarithms with and without a calculator.
Solve logarithmic equations

2. Exponential vs. Logarithmic form
Exponential Form
Logarithmic Form

3. Ex 1) Change each exponential expression to an equivalent expression involving a logarithm:

4. Ex 2) Change each logarithmic expression to an equivalent expression involving an exponent:

5. Ex 3) Find the exact value of each:

6. Domain and Range of Log functions!
Domain of a logarithmic function = range of the exponential function = (0,∞)
Range of a logarithmic function = domain of the exponential function = (-∞, ∞)
Ex 4) Find the domain of each logarithmic function:

7. Properties of a Logarithmic Function:
The domain is the set of positive real numbers; the range is all real numbers.
The x-intercept of the graph is 1. There is no y-intercept.
The y-axis (x = 0) is a vertical asymptote of the graph.
A logarithmic function is decreasing if 0 < a < 1 and increasing if a > 1.
The graph of f contains the points (1, 0), (a, 1) and (1/a, -1).
The graph is smooth and continuous, with no corners or gaps or holes.

8. Ex 5) Solve the following equations: