Answer to Question #192674 in Algebra for will

Question

Solving Exponential Equations Practice:

1. 8^x-3 =8⁵
2. 10^3x+2 = 10¹¹
3. 4^6x = 16⁹

Answer 1

1.

$$8^{x-3}=8^5$$

Exponential equation function is monotone

$$x-3=5$$

$$x=8$$

2.

$$10^{3x+2}=10^{11}$$

Exponential equation function is monotone

$$3x+2=11$$

$$3x=9$$

$$x=3$$

3.

$$4^{6x}=16^9$$

$$4^{6x}=(4^2)^9$$

$$4^{6x}=4^{2\cdot9}$$

$$4^{6x}=4^{18}$$

Exponential equation function is monotone

$$6x=18$$

$$x=3$$