Download 4.8 Solve Exponential and Logarithmic Inequalities

4.8
Solve Exponential and
Logarithmic Inequalities
Test 2 Unit 4 over 4.6-4.9
on
Wednesday 2/16/2011
Solving Exponential Inequalities…
Let’s review exponentials

Remember what an exponential graph looks
x
like? Graph y  2

Solve.
2 x 5  8
2 x 2  8
Example 1:

Solve 4x + 1 > 32



Step 1: Write the equation that corresponds to
inequality.
Step 2: Solve for x.
Step 3: plot the x-value on a number line and
test intervals or use your knowledge of the
graph.
OR
Asymptote?
Example 1:
 Solve
4x + 1 > 32
[1.5, ∞)
You Try:
1.
Solve the exponential inequality
32x – 1 < 4
2.
73x – 4 < 18

Solving Logarithmic Inequalities…

Remember what an logarithmic graph looks like?
y  log x
Graph

Solve.
log 7 x  3
1
log x  2
9
log 6 216  x
Example 2:

1.
Solve the logarithmic inequality
log5x < 2



Step 1: Write the corresponding equation
Step 2: solve for x.
Step 3: plot the x-value on a number line and
test intervals or use your knowledge of the
graph.
OR
Asymptote?
Example 2:

1.
Solve the logarithmic inequality
log5x < 2
(0, 25)
Example 2 Cont’d:

2.
Solve the logarithmic inequality
log4x + 8 > 11
[64, ∞)
You Try:
1.
Solve the logarithmic inequalities
log62x + 7 < 10
2.
log9(x – 8) < 3/2

HOMEWORK
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