Solve for the values of x for each of the following exponential equations and inequalities. 1. 82− = 2
3. 5 = 25−2
4. 3+2 ≥ 27
5. 43 = 8−1

8

2−x

=2

8^{2-x}=8^{1/3}8

2−x

=8

1/3

2-x=\dfrac{1}{3}2−x=

3

1

x=\dfrac{5}{3}x=

3

5

2.

(\dfrac{1}{2})^{x}<\dfrac{1}{8}(

2

1

)

x

<

8

1

(\dfrac{1}{2})^{x}<(\dfrac{1}{2})^{3}(

2

1

)

x

<(

2

1

)

3

x>3x>3

3.

5^x=25^{x-2}5

x

=25

x−2

25^{x/2}=25^{x-2}25

x/2

=25

x−2

\dfrac{x}{2}=x-2

2

x

=x−2

\dfrac{x}{2}=2

2

x

=2

x=4x=4

4.

3^{x+2}\geq273

x+2

≥27

3^{x+2}\geq3^33

x+2

≥3

3

x+2\geq3x+2≥3

x\geq1x≥1

5.

4^{3x}=8^{x-1}4

3x

=8

x−1

2^{6x}=2^{3x-3}2

6x

=2

3x−3

6x=3x-36x=3x−3

3x=-33x=−3

x=-1x=−1

Step-by-step explanation:

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(−$11) ⋅ 12

deductions are negative and there are 12 months in a year