One-to-One Property...3

[nycmathguy]

Section 3.1
25 & 27

Question 25

3^(x + 1) = 27

Let 27 be 3^3.

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

x + 1 = 3

x = 3 - 1

x = 2

Let me see if it's true.

3^(x + 1) = 27

Let x = 2.

3^(2 + 1) = 27

3^(3) = 27

27 = 27

Yep!

Question 27

(1/2)^x = 32

(1^x)/(2^x) = 32

1 raised to any power is one.

So, 1^(x) = 1.

1/(2^x) = 32

The left can be written as 2^(-x).

2^(-x) = 32

Let 32 be 2^5.

2^(-x) = 2^5

-x = 5

x = 5/-1

x = -5

Let me check.

(1/2)^x = 32

Let x = -5

(1/2)^(-5) = 32

(1^-5)/(2^-5) = 32

1/(2^-5) = 32

The left side can be written as 2^5.

2^5 = 32

32 = 32

Yep! It also checks to be true.

 

[MathLover1]

correct

 

[nycmathguy]

correct

Very good.