How do I solve exponential equations and inequalities?

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Presentation transcript:

How do I solve exponential equations and inequalities?

4.6 Solve Exponential Equations and Inequalities Example 1 Solve by equating exponents Write original equation. Rewrite each power with a base __. 4 Power of a power property. Property of equality. Solve for x. The solution is ___. 2 Check Substitute the solution into the original equation. 2 2

4.6 Solve Exponential Equations and Inequalities Checkpoint. Complete the following exercises.

4.6 Solve Exponential Equations and Inequalities Example 2 Solve an exponential equation by graphing The graphs intersect only once, when x = ___. 2 So, ___ is the only solution. 2

4.6 Solve Exponential Equations and Inequalities Checkpoint. Complete the following exercises.

4.6 Solve Exponential Equations and Inequalities Example 3 Solve an exponential inequality Write original equation. Rewrite each power with a base __. 3 Power of a power property. Because f( x ) = 3 x is an increasing function, f( x 1 ) < f( x 2 ) implies that x 1 < x 2. Solve for x.

4.6 Solve Exponential Equations and Inequalities Example 3 Solve an exponential inequality Solve for x. Substitute z = 2. Check Check that the solution is reasonable by substituting several values into the original inequality. Substitute z = 4. Because z = __ is a solution of the inequality and z = __ is not, the solution z < ___ is reasonable. 24 3

4.6 Solve Exponential Equations and Inequalities Checkpoint. Complete the following exercises.

4.6 Solve Exponential Equations and Inequalities Example 4 Solve an exponential inequality by graphing The graphs intersect only once, when x = ______ The graph of y = 3 2x  1 – 3 is ______ the graph of y = 0.75 when _______ above x > 1.10 The solution is _________. x > 1.10

4.6 Solve Exponential Equations and Inequalities Checkpoint. Complete the following exercises.

4.6 Solve Exponential Equations and Inequalities Pg. 144, 4.6 #1-19