Logarithmic functions are the inverse of exponential functions. They allow mathematicians to write exponential expressions like 2x = 6 in logarithmic form as log2 6 = x. The graph of a logarithmic function y = logb(x - h) + k will increase if b > 1 and decrease if 0 < b < 1. It will have a vertical asymptote at x = h. Logarithmic functions have the opposite domain and range from their inverse exponential functions.

1. Logarithmic FunctionsAlgebra 28.4

2. Logarithmic Functions2x = 6You know that 22< 6 < 23, so that means 2 < x < 3.

3. Mathematicians use logarithms to find the exact value of exponents like this example.

4. 2x = 6 can also be written in log form:log2 6 = x

5. 2x = 6 can also be written in log form:log2 6 = xExponential formLogarithmic form

6. Log FunctionsLog functions are inverses of exponential functions.

7. The graphs of inverse functions are symmetric across the line y = x.

8. The Domain and Range for exponential functions are opposite for log functions.

9. Graphing Log FunctionsThe line x = h is a vertical asymptote.

10. Graphing Log FunctionsThe line x = h is a vertical asymptote.If b > 1, the graph is increasing.

11. y = logb (x – h) + kGraphing Log FunctionsThe line x = h is a vertical asymptote.If b > 1, the graph is increasing.If 0 > b > 1, the graph is decreasing.