Order the steps to solve the equation log3(x + 2) = log3(2x2 − 1) from 1 to 6.

0 = (2x − 3)(x + 1)

0 = 2x2 − x −3

Potential solutions are −1 and 3
2
.

2x − 3 = 0 or x + 1 = 0

x + 2 = 2x2 − 1

3log3(x + 2) = 3log3(2x2 − 1)

Step 1

log3(x + 2) = log3(2x² − 1)

Step 2

x + 2 = 2x² - 1

Step 3

2x² - x - 3 = 0

Step 4

(2x - 3)(x + 1) = 0

Step 5

2x - 3 = 0 or x + 1 = 0

Step 6:

Potential solutions are -1 and 3/2

Step-by-step explanation:

Step 1

log3(x + 2) = log3(2x² − 1)

Step 2

x + 2 = 2x² - 1

Step 3

2x² - x - 3 = 0

Step 4

2x² - 3x + 2x - 3 = 0

x(2x - 3) + 1(2x - 3) = 0

(2x - 3)(x + 1) = 0

Step 5

2x - 3 = 0 or x + 1 = 0

Step 6:

x = 3/2 or x = -1

Potential solutions are -1 and 3/2

-2

7 - 9 = -2

reversed:

-2 + 9 = 7