Algebra and Trigonometry, 5th Edition

5.3 Logarithmic Functions and Graphs

• Find common logarithms and natural logarithms with and without a calculator.

• Convert between exponential equations and logarithmic equations.

• Change logarithmic bases.

• Graph logarithmic functions.

• Solve applied problems involving logarithmic functions.

We now consider logarithmic, or logarithm, functions. These functions are inverses of exponential functions and have many applications.

Logarithmic Functions

We have noted that every exponential function (with $a>0$ and $a\ne 1$) is one-to-one. Thus such a function has an inverse that is a function. In this section, we will name these inverse functions logarithmic functions and use them in applications. We can draw the graph of the inverse of an exponential function ...