What is the value of x in the equation log (4x) = 3?

A. 250
Correct! Graph the left side and the right side on your graphing calculator. The intersection is (250,3). Therefore the answer is 250.

B. 3
Incorrect. That’s the y-coordinate of the point of intersection. You need the x-coordinate.

C. 5.6
Incorrect. You solved for 4log (x) = 3.

D. No real solution
Incorrect. There is a solution to this equation. Graph the left side and the right side on your graphing calculator to find the intersection.

How many solutions are there to the equation log (x² + 4) = 2?

A. 0
Incorrect. If you graph both sides of the equation on your graphing calculator, you will see that there are two points of intersection, so there are two solutions.

B. 1
Incorrect. If you graph both sides of the equation on your graphing calculator, you will see that there are two points of intersection, so there are two solutions.

C. 2
Correct! The graph of y = log (x^2 + 4) intersects with the graph of y = 2 two times, therefore, there are 2 solutions to the equation.

D. Infinitely many
Incorrect. Graph the left side and the right side on your graphing calculator to check the number of solutions.

Solve for x: log₃ (x - 10) + log₃ (x + 2) = 4

A. No real solutions.
Incorrect. There are two real solutions although one is an extraneous solution.

B. -6.8, 14.8
Incorrect. You cannot simplify the log expression before solving graphically or with a table. It leads to extraneous solutions.

C. 104.2
Incorrect. You used common logs instead of logs with base 3.

D. 14.8
Correct! Graph left side and the right side on your graphing calculator to find the intersection remembering the domain has to be greater than zero therefore there is one solution.

Solve for x: log₅ (x − 1) − log₅ (x + 1) = log₅ x

A. 1.6
Incorrect. You may have incorrectly entered the left side of the equation.

B. 1
Incorrect. You may have incorrectly entered the left side of the equation.

C. 3.1
Incorrect. You may have incorrectly entered the left side of the equation.

D. No real solution
Correct! If you graph the left side and the right side of the equation, the two curves never intersect, indicating that there is no solution.