Question

Solve for the values of x for each of the following exponential equations and inequalities.

1. 82-2

2. () <=

3. 5* = 25-2

4. 3x+2 à ¢ ‰ ¥ 27

5. 43x 8-1

Answer 1

1.

$$8^{2-x}=2$$

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

$$2-x=\dfrac{1}{3}$$

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

2.

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

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

$$x>3$$

3.

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

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

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

$$\dfrac{x}{2}=2$$

$$x=4$$

4.

$$3^{x+2}\geq27$$

$$3^{x+2}\geq3^3$$

$$x+2\geq3$$

$$x\geq1$$

5.

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

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

$$6x=3x-3$$

$$3x=-3$$

$$x=-1$$