Exponential Equation of Linear Form

Solve the following exponential equations

1. a) (1/2) ^x = 8 b) (0.25) ^x+1 = 16
2. c) 3^x = 1/81 d) 10 ^x = 1/0.001
3. e) 4/2^x = 64 ^x

Solution

1. a) (1/2) ^X = 8

(2 ^-1) ^x = 2 ³

2 ^–x = 2 ³

-x = 3

X = – 3

1. b) (0.25) ^x+1 = 16

(25/100) ^x+1 = 16

(1/4) ^x+1 = 4 ²

(4 ^-1) ^x+1 = 4 ²

– x – 1 = 2

– x = 2 + 1

– x = 3

X = – 3

1. c) 3^x = 1/81

3^x = 1/3⁴

3^x = 3 ^-4

X = -4

1. d) 10^x = 1/0.001

10 ^x = 1000

10 ^x = 10 ³

10^x = 10 ³

X = 3

1. e) 4/2^x = 64 ^x

4÷2^x = 64 ^x

2² ÷2^x = 64 ^x

2 ^2-x = (2 ⁶) ^x

2 ^2-x = 2 ^6x

2-x  = 6x

2=6x+x

2 = 7x

Divide both sides by 7

2/7 = 7x/7

X = 2/7

EVALUATION ( USE THE DISCUSSION BOX AT THE BOTTOM TO SUBMIT YOUR ANSWER FOR DISCUSSION AND APPRAISAL)

Solve the following exponential equations

1. a) 2 ^x = 0.125 b) 25 ^(5x) = 625    c)            10 ^x = 1/100000