LOGARITHMIC FUNCTIONS Solving Logarithmic Inequalities (Page 2 of 2)

We now interpret the inequality LOGbase2(x+5)-3+LOGbase2(x-2) < 0 in terms of the function that is graphed. The solution set will be all values of x for which the function Y1 has negative y-values. Let's use TRACE to identify where these values of x are.

TRACE key. Left arrow key....

Right arrow key....

 Calculator screen image. Calculator screen image.

Since the x-intercept has a y-value equal to 0, it is NOT part of the solution set. The x-values to the left of 3 produce negative y-values. The inequality LOGbase2(x+5)-3+LOGbase2(x-2) < 0 means that the graph of Y1 must lie below the x-axis. Looking at the graph, we see this is true if x is to the left of 3. We must also consider the domain of this function, which is x > 2. The inequality is not defined for values of x less than or equal to 2. So, the solution set is {x: 2 < x < 3}, or in interval notation, (2, 3).
Copyright © 2010 Turner Educational Publishing
Go back to the previous page. Go to the next page. Go to the Table of Contents. Go to the Index page. Go to the Quiz page. Exit to the Home page.