Aladdin is solving the log equation log (x) + log (x + 3) = 1 for x. His solution is below.
| log(x) + log(x + 3) = 1 | |
| Apply the product property. | log[x(x + 3)] = 1 |
| Change from log to exponential form. | 101 = x(x + 3) |
| Distribute and simplify. | x2 + 3x − 10 = 0 |
| Factor. | (x + 5)(x − 2) = 0 |
| Solve for x. | x = -5 or x = 2 |
Jasmine comes along and looks at Aladdin's solution and informs him that his solution is incorrect. In your notes, explain to Aladdin what he did incorrectly.
Now it's Jasmine's turn to solve a log equation. The equation she has to solve is log x + log 2 = log 5. Her solution is below:
| log x + log 2 = log 5 | |
| Domain: x > 0 | |
| Combine the logarithms on the left. | log (x + 2) = log 5 |
| Since the 2 sides are equal, eliminate the logs. | x + 2 = 5 |
| Solve for x. | x = 3 |
When Aladdin checks Jasmine's paper, he tells her she made a mistake. In your notes, explain to Jasmine what mistakes she made.