Section 13.1 Evaluating Logarithmic Functions
Example 13.1. Exploring and Motivation.
Suppose
So, we have
Let's do another. What is the inverse of
So, we have
One more: what is the inverse of
So, we have
So what do we do with something like
Definition 13.2.
If
Example 13.3.
Suppose
Suppose
Checkpoint 13.4.
Find the inverse of each function below.
Since
is an exponential function, its inverse will be a logarithm. The bases need to match, soSince
is an exponential function, its inverse will be a logarithm. The bases need to match, soSince
is a logarithm, its inverse will be an exponential function. The bases need to match, soSince
is a logarithm, its inverse will be an exponential function. The bases need to match, so
Example 13.5.
Let's evaluate each of the following expressions.
-
Suppose we want to evaluate
Since the log is base 7, and so is the exponential, so they cancel and we get that -
Suppose we want to evaluate
Since the log is base 4, and so is the exponential, so they cancel and we get that -
Suppose we want to evaluate
Since the log is base 6, and so is the exponential, so they cancel and we get that -
Suppose we want to evaluate
At first glance, the inside is not an exponential with the right base (3). But, all hope is not lost, since 9 is actually a power of 3. Since
Checkpoint 13.6.
Simplify each of the following, if possible
Simplify each of the following, if possible
-
Since the log is base 8, and so is the exponential, so they cancel and we get that -
Since the log is base 3, and so is the exponential, so they cancel and we get that -
At first glance, the inside is not an exponential with the right base (2). But, all hope is not lost, since 8 is actually a power of 2. Since Since 9 is not a power of 7, this one cannot be simplified any further.