Solving Exponential Equations (Mr.Ty's Bday)

MILD

100

2²ˣ = 2¹⁰

2²ˣ = 2¹⁰ → 2x = 10

 x = 5

200

5³ˣ = 5¹⁵

5³ˣ = 5¹⁵ → 3x = 15 → 

x = 5

300

7ˣ⁺⁴ = 7¹¹

7ˣ⁺⁴ = 7¹¹ → x + 4 = 11 → 

x = 7

400

9ˣ⁻² = 9⁷

9ˣ⁻² = 9⁷ → x − 2 = 7 → 

x = 9

500

3^x+1 = 3¹⁰

3ˣ⁺¹ = 3¹⁰ → x + 1 = 10 → 

x = 9

MEDIUM

100

3ˣ = 9⁴

3ˣ = 9⁴ → 

9 = 3² →

 3ˣ = (3²)⁴ → 

3ˣ = 3⁸ → 

x = 8

200

5ˣ = 25⁴

5ˣ = 25⁴ →

 25 = 5² → 

5ˣ = (5²)⁴ → 

5ˣ = 5⁸ → 

x = 8

300

2ˣ = 32³

2ˣ = 32³ 

→ 32 = 2⁵ 

→ 2ˣ = (2⁵)³ 

→ 2ˣ = 2¹⁵ 

x = 15

400

3ˣ = 27⁴

3ˣ = 27⁴ → 

27 = 3³ → 

3ˣ = (3³)⁴ → 

3ˣ = 3¹² → 

x = 12

500

2ˣ = 128³

2ˣ = 128³ → 

128 = 2⁷ → 

2ˣ = (2⁷)³ → 

2ˣ = 2²¹ → 

x = 21

SPICY

100

9ˣ⁺² = 27ˣ

9ˣ⁺² = 27ˣ

9 = 3², 27 = 3³ → (3²)ˣ⁺² = (3³)ˣ

3²ˣ⁺⁴ = 3³ˣ → 

2x + 4 = 3x → 

x = 4

200

25ˣ⁻² = 125ˣ

25ˣ⁻² = 125ˣ

25 = 5², 125 = 5³ → (5²)ˣ⁻² = (5³)ˣ

5²ˣ⁻⁴ = 5³ˣ → 2x − 4 = 3x →

x = −4

300

(1/6)^x+2 = 36

(1/6)ˣ⁺² = 36

36 = 6², (1/6) = 6⁻¹ → 

6^-(x+2) = 6² → 

−x − 2 = 2 → 

x = −4

400

(1/5)^x-1 = 125

(1/5)^x-1 = 125

125 = 5³, (1/5) = 5⁻¹ → 

5⁻^-(x-1) = 5³ → 

−x + 1 = 3 → 

x = −2

500

(1/3)^x-2 = 9

(1/3)^x-2 = 9

9 = 3², (1/3) = 3⁻¹ → 

3^-(x−2) = 3² → 

−x + 2 = 2 → x = 0

MR.TY

100

How old is Mr. Ty turning?

31!

200

Where was Mr. Ty Born?

Colorado!

300

Mr. Ty raises this animal at home

ducks!

400

Mr. Ty's major in college?

Anthropology!

500

Mr. Ty's Hobbies include... (x3)

Guitar, Painting, Gardening, Fishing,