PRACTICE PROBLEMS ON SOLVING EXPONENTIAL EQUATIONS

Solve the following equation.

(1) 4^2x+3 = 1

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

(3) 3^1-2x = 243

(4) 3^2a = 3^-a

(5) 4^3x-2 = 1

(6) 4^2p = 4^-2p-1

(7) 6^-2a = 6^2-3a

(8) 2^2x+2 = 2^3x

(9) 6^3m ⋅ 6^-m = 6^-2m

(10) 2^x/2^x = 2^-2x

(11) 10^-3x ⋅ 10^x = 1/10

(12) 3^-2x+1 ⋅ 3^-2x-3 = 3^-x

Solution

1) 2x^(2/3) = 8

2) 4x^(3/2) = 32

3) x^1/4 + 3 = 0

4) 2x^3/4 - 14 = 40

5) (x + 6)^1/2 = x

6) (5 - x)^1/2 – 2x = 0

7) 2(x + 11)^1/2 = x + 3

8) (5x² – 4)^1/4 = x

9) x^1/5 = 2

10) 2√(3x – 1) + 3 = 11

11) 4x² = 64

12) 2(x – 2)⁴ – 3 = 159

13) √(2x + 4) = √(x + 2)

14) ∛x – 6 = -2

Solution

Solve the following and find extraneous solutions.

1) (2x)^3/4 + 2 = 10

2) (x + 30)^1/2 = x

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

4) (x + 6)^1/2 = x

5) (x + 2)^3/4 = 8

Solution

Solve the Following

(1) If 3^a+1 = 3^-a+7, what is the value of a ? Solution

(2) If 3^x+2 = y, then what is the value of 3^x in terms of y ?

(a) y+9 (b) y-9 (c) y/3 (d) y/9

Solution

(3) If 2a-b = 4, what is the value of 4^a/2^bSolution

(4) If 2^x+3 - 2^x = k(2^x), what is the value of k ? Solution

(5) If

√(x√x) = x^a

then what is the value of a ? Solution

(6) If n³ = x and n⁴ = 20x, where n > 0, what is the value of x ?

Solution

(7) Solve for x, 2(4^2x+1) = 128 Solution

(8) 12^2x-1 = (∜12)^xSolution

(9) 3^4x+3 = 81^xSolution

(10) 12 ⋅ 2^x-7 = 24 Solution

PRACTICE PROBLEMS ON SOLVING EXPONENTIAL EQUATIONS

Solve the Following

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