exponential functions.!!!!!!!!!!!!!!!

Question

1. 32^(2x-3) = 2

2. 9^(2x+1) = 81

3.1/4 = 2^3x

Answer 1

1. 32^(2x-3) = 2

2^5(2x-3) = 2^1

since the bases are equal so the powers are equal.

5(2x-3) = 1

10x - 15 = 1

Add 15 to each side.

10x - 15+15 = 1+15

10x  = 16

Divide each side by 2.

5x = 8

x = 8/5

The solution is x = 8/5

Answer 2

2. 9^(2x+1) = 81

3^2(2x+1) = 3^4

Since the bases are equal so the powers are equal.

2(2x+1) = 4

4x + 2 = 4

Subtract 2 from each side.

4x + 2 -2= 4-2

4x  =  2

Divide each side by 2.

4x/2 = 2/2

2x = 1

x = 1/2

The solution is x =1/2

 

Answer 3

3.1/4 = 2^3x

1/(2^2) = 2^3x

2^(-2) = 2^3x

Since the bases are equal so the powers are equal.

-2 = 3x

Divide each side by 3.

3x/3 = -2/3

x = -2/3

The solution is x = -2/3