HONORS ALGEBRA 2 : Problems on Solving Exponential Equations

Solve each of the following equations without using calculator.

Problem 1 :

5x = 625

Solution :

5x = 625

625 is a power of 5 and it can be written as 54.

5x = 54

Since the base is same on both sides, exponents can be equated.

x = 4

Problem 2 :

Solution :

Problem 3 :

Solution :

Problem 4 :

3x - 10 = 27x

Solution :

3x - 10 = 27x

3x - 10 = (33)x

3x - 10 = 33x

x - 10 = 3x

2x = 10

x = 5

Problem 5 :

4x + 2 = 8x

Solution :

4x + 2 = 8x

(22)x + 2 = (23)x

22(x + 2) = 23x

2(x + 2) = 3x

2x + 4 = 3x

4 = x

Problem 6 :

Solution :

x2 + 1 = 2x

x2 - 2x + 1 = 0

Solve by factoring.

x2 - x - x + 1 = 0

x(x - 1) - 1(x - 1) = 0

(x - 1)(x - 1) = 0

(x - 1)2 = 0

Taking square root on both sides,

x - 1 = 0

x = 1

Problem 7 :

Solution :

2(x + 4) = 3x2

3x- 2x - 8 = 0

Solve by factoring.

3x- 6x + 4x - 8 = 0

3x(x - 2) + 4(x - 2) = 0

(x - 2)(3x + 4) = 0

x - 2 = 0  or  3x + 4 = 0

x - 2 = 0

x = 2

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