Shifts in Logarithms

Write log_b(xy) as two logs

• log_bx+log_by

• log_bx-log_by

• log_bx*log_by

• log_bx/log_by

Use the properties of logarithms to retwrite

• A

• B

• C

• D

Condense

• logxyz³

• log(xy/z³)

• logx+logy+logz³

• logx³y³z³

Expand

• A

• B

• C

• D

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

Match the following log functions to their horizontal shift (which way will the asymptote shift)

• No Horizontal Shift

• Shift Right

• Shift Left

Write the equation of the graph.

• f(x) = log ₂(x) + 3

• f(x) = log₂ (x) - 3

• f(x) = log₂ (x+3)

• f(x) = log₂(x-3)

Identify the transformation that makes the graph shift horizontally to the left fifteen units.

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

Which graph matches the function

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

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