Shifts in Logarithms

Write log_b(xy) as two logs

Use the properties of logarithms to retwrite

Condense

Expand

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.)

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

Write the equation of the graph.

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.)

Which graph matches the function

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