Practice Test

Question 15 • Mathematics III

Which graph shows the solution to the equation? log sub 3 of open paren x plus 2 close paren is equal to 1

Answer

Image with description Coordinate plane with x-axis and y-axis. A logarithmic-shaped curve begins near the y-axis at x equals 0 and extends to the right. The curve passes through 1 comma 0, rises gradually through approximately 3 comma 1 and 9 comma 2, and continues increasing as x increases. A horizontal line y equals negative 1 extends across the graph with arrows on both ends. The curve intersects the horizontal line near 0.3 comma negative 1 and lies above the line for x values greater than this point. Both the curve and the horizontal line continue indefinitely as indicated by arrows.

Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (8 comma 1) and increases as x increases. There is a line that is parallel to the x axis and cuts the y axis at (0 comma 1).

Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (1 comma 1) and increases as x increases. There is a line parallel to the x axis and cuts the y axis at (0 comma 1).

Explanation

Rewrite the equation in exponential form: log₃(x + 2) = 1 means x + 2 = 3¹ = 3, so x = 1. The graph of y = log₃(x + 2) passes through (1, 1), and the equation’s right side is the horizontal line y = 1. Choice C shows that curve and line intersecting at (1, 1).

AI-written and checked against the verified answer.

More from this Course

Practice Test

Practice Test

Practice Test