Nayland College - Mathematics Home . Year 9 . Year 10 . Level 1 . Level 2 . L3 Statistics . L3 Maths . L3 Calculus . About . Links

# Graphing Log Functions

 Logarithmic Functions Basic Log graphs with different bases, such as y = Log2(x) How the base changes the graph shape Relating the Log graph to the exponential graph Remember to define the Domain if you write the equation for a Log graph. Ex12.07 p54, More Log Graphs Vertical and horizontal translation of log graphs Log and exponential applications

# Basic log graph

The log graph is a reflection of an exponential graph in the line y = x

x y
3
2
1
0
-1
-2

# Different bases

A different base changes the shape of the graph

y = log2x

Features

Features

Features

# Inverted log graph

A negative multiplier inverts the graph about the x axis

y = log2x

Features

# Vertical shift

Adding a constant vertically translates the log graph

y = log2x

Features

Features

Features

# Horizontal shift

Adding a constant to x horizontally translates the log graph

y = log2x

Features

Features

Features

# Combined shifts

Horizontal and vertical shifts can be combined

y = log2x

Features

Features

Features