Exponential and Logarithmic Inequalities Answers
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3
In order for the pH level of an acidic substance to be less than 2.25, the molar concentration of hydrogen ions, x, in the substance must satisfy the inequality –log x < 2.25. Review the table of values representing the left side of the inequality.
A
(0, 0.005623)B
(0.005623, ∞)C
(0, 0.0005623)D
(0.0005623, ∞)4
Jeff wants to solve log2(x + 1) ≤ log3(x + 6). He draws the graphs of the related inequalities as shown and states that the solution set is (–1, 3].
A
The graphs are correct, and the solution set is correct.B
The graphs are correct, but the solution set is incorrect.C
The graphs are incorrect, but the solution set is correct.D
The graphs are incorrect, and the solution set is incorrect.5
What is the solution set to log8(4x + 2) + 4 ≥ 5?
A
(–0.5, ∞)B
[1.5, ∞)C
(1.5, ∞)D
[5, ∞)6
Alondra creates a table of values for a logarithmic function.
A
(–3, –1)B
(–1, 2)C
(–1, ∞)D
(2, ∞)7
What is the solution set to 8(2x – 3) ≤ 20 – 4x?
A
(–∞,∞)B
(–∞, 2]C
(0, 20)D
[2, ∞)8
Review the graph of y ≥ 4x – 4.
A
(–∞, 5]B
(–∞, 4]C
(0, 4]D
[5, ∞)10
Which set of graphs can be used to find the solution set to 3 log2(x + 4) < 6?
A
On a coordinate plane, a dotted line is at y = 6. Everything above the line is shaded. A dotted line curve approaches x = negative 4 in quadrant 3, and curves up through (negative 3, 0) and (0, 6). Everything above the curve and to the right of x = negative 4 is shaded.
B
On a coordinate plane, a dotted line is at y = 6. Everything above the line is shaded. A dotted line curve approaches x = negative 4 in quadrant 3, and curves up through (negative 3, 0) and (0, 6). Everything below and to the right of the curve is shaded.
C
On a coordinate plane, a dotted line is at y = 6. Everything below the line is shaded. A dotted line curve approaches x = negative 4 in quadrant 3, and curves up through (negative 3, 0) and (0, 6). Everything below and to the right of the curve is shaded.
D
On a coordinate plane, a dotted line is at y = 6. Everything below the line is shaded. A dotted line curve approaches x = negative 4 in quadrant 3, and curves up through (negative 3, 0) and (0, 6). Everything above the curve and to the right of x = negative 4 is shaded.
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