Transforming Logarithms

Condense

• log₈(a¹⁸/b³)

• log₈(a¹⁸b³)

• log₈(a/b³)

• 15log₈(a/b³)

Expand

• A

• B

• C

• D

• log (xy³)
• log (x⁶ − y³)
• log (x⁶/y³)
• log (x⁶ + y³)

• 6log₈(xyz)
• log₈(x) - log₈(y) - 6log₈(z)
• log₈(x) + log₈(y) - log₈(z)
• log₈(x) + log₈(y) + 6log₈(z)

How has the graph transformed?

Red is parent graph

Blue is transformation

• left 1 up 6

• left 2 up 4

• left 2 up 6

• up 6

Write the equation of a natural logarithmic function that has been shifted two units to the left, one unit up, and vertically stretched by a factor of three.

(Begin your answer with "y=." Use parentheses where necessary.)

Mathematical Equivalence

ON

Describe the transformation of y=ln(x) that would give the graph for y = ln(x+7)

• vertical translation 7 up

• vertical translation 7 down
  vertical stretch by a factor of 7

• horizontal translation 7 left

• horizontal translation 7 right

Write the equation of a natural logarithmic function that has been shifted two units to the left, one unit up, and vertically stretched by a factor of three. (Begin your answer with "y=." Use parentheses where necessary.)

Mathematical Equivalence

ON

Describe the transformations of f(x)= -log₂(x+1)

• left 1

• left one & reflected over the y-axis

• left one & reflected over the x-axis

• right one & reflected over the x axis

• left 3, right 1

• right 3, down 1

• right 3, up 1

• left 3, down 1