Logarithmic Mastery Check

Solve the logarithmic equation: log₂(x) + log₂(x - 2) = 3

• x = 1 or x = 8

• x = 2 or x = 6

• x = 4 or x = 8

• x = 6 or x = 10

Evaluate the expression: log₅(125)

• 2

• 3

• 5

• 25

Graph the logarithmic function: y = log₃(x - 2). Which of the following is true?

• The graph passes through the point (5, 1)

• The graph has an asymptote at x = 2

• The graph intersects the y-axis at y = -1

• The graph is decreasing for all values of x

Solve the logarithmic equation: log(x² - 6x) = 2

• x = 8

• x = 3 ± √13

• x = 4 or x = 2

• x = 6 or x = -1

Evaluate the expression: log₇(1/49)

• -½

• -2

• ½

• 2

Graph the logarithmic function: y = -2log(x). Which of the following is true?

• The graph is reflected over the x-axis

• The graph passes through the point (1, -2)

• The graph has an asymptote at y = 0

• The graph is increasing for all values of x

Solve the logarithmic equation: 5log(x) - log(2) = 3

• x = 2^(3/5)

• x = 10^(3/5)

• x = 5^(3/5)

• x = (2/5)^(3/5)

Evaluate the expression: log₄(16) + log₄(2)

• 3

• 4

• 5

• 6

Graph the logarithmic function: y = log(x) + 2. Which of the following is true?

• The graph has a vertical shift upwards by 2 units

• The graph has a horizontal shift to the right by 2 units

• The graph has an asymptote at y = 2

• The graph passes through the point (1, 2)

Solve the logarithmic equation: log₃(x + 1) - log₃(x - 1) = 1

• x = 2

• x = 3

• x = 4

• x = 5