Question

Solve the following exponential equations and inequalities. (3 points each) 1.52x+1 = 125 4.7x+2 < 49* 2.7x+2 1 x 49 = 5.22x≤8 3.125-125

Answer 1

1.

$$5^{2x+1}=125$$

$$2x+1=3$$

$$2x=2$$

$$x=1$$

2.

$$7^{x+2}<1$$

$$7^{x+2}<7^0$$

$$7>1=>x+2<0$$

$$x<-2, x\in(-\infin, -2)$$

3.

$$5^{-x}<125$$

$$5^{-x}<5^3$$

$$5>1=>-x<3$$

$$x>-3, x\in(-3, \infin)$$

4.

$$7^{x+2}<49$$

$$7^{x+2}<7^2$$

$$7>1=>x+2<2$$

$$x<2, x\in(-\infin, 0)$$

5.

$$2^{2x}<8$$

$$2^{2x}<2^3$$

$$2>1=>2x<3$$

$$x<3/2, x\in(-\infin, 3/2)$$