Transformations of Logs

Use multiple log properties to write as a single log:
log₂x -  5log₂y

• log₂(x/y⁵)

• log₂(xy⁵)

• log₂(x/y)⁵

• log₂(x/5y)

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

Rewrite log_b(xⁿ)

• nlog_bx

• (log_bx)ⁿ

• xⁿlog_bx

• log_b(xⁿ)

Change to Exponential Form:
log₆36 = 2

• 2⁶=36

• 6²=36

• 36²=6

• 36⁶=2

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

• left 3, right 1

• right 3, down 1

• right 3, up 1

• left 3, down 1

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

Use y=log(x) as a parent function. To graph y=log(x-4)+7, the parent function should be translated vertically ​ (a)   (up or down) by ​ ​ (b)   units. The vertical asymptote should be shifted horizontally to the ​ (c)   (left or right) by ​ (d)   units.

• up

• right

• 4

• down

• left

• 7

Which graph matches the function

*remember the transformation has shifted it right 3 and down 3

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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

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