Question

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

inequalities.

1. 6𝑥+2 = 362𝑥−3

2. 5𝑥−1 = 625

3. 54𝑥 ≥ 253𝑥+2

Answer 1

1.

$$6^{x+2}=36^{2x-3}$$

$$x+2=2(2x-3)$$

$$3x=8$$

$$x=8/3$$

2.

$$5^{x-1}=625$$

$$5^{x-1}=5^4$$

$$x-1=4$$

$$x=5$$

3.

$$5^{4x}\ge25^{3x+2}$$

$$4x\ge2(3x+2)$$

$$2x\le-4$$

$$x\le -2$$