LOGARITHMIC FUNCTIONS Solving Logarithmic Inequalities (Page 1 of 2)

Solving a logarithmic inequality is nearly the same as solving an equation. In fact, we solve the equation first using the x-intercept method, then analyze the graph to determine the solution set of the inequality.

To solve the inequality LOGbase2(x+5) < 3-LOGbase2(x-2), first get a zero on the right:
 LOGbase2(x+5)-3+LOGbase2(x-2) < 0. Then replace the inequality symbol with an equal sign:
 LOGbase2(x+5)-3+LOGbase2(x-2) = 0. This equation was solved in the previous example using CALC zero and the solution was determined to be x = 3. The graph of the function represented by the left side of the equation,
 f(x) = LOGbase2(x+5)-3+LOGbase2(x-2), is shown along with the zero.

GRAPH key. Calculator screen image.
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