6.05 Graphs of logarithmic and exponential functions

Interactive practice questions

Consider the function $y=\log_4x$y=log4x, the graph of which has been sketched below.

Loading Graph...

Complete the following table of values.

$x$`x`	$\frac{1}{16}$116	$\frac{1}{4}$14	$4$4	$16$16	$256$256
$y$`y`	$\editable{}$	$\editable{}$	$\editable{}$	$\editable{}$	$\editable{}$

Determine the $x$x-value of the $x$x-intercept of $y=\log_4x$y=log4x.

How many $y$y-intercepts does $\log_4x$log4x have?

Determine the $x$x value for which $\log_4x=1$log4x=1.

Easy

3min

Consider the two graphs sketched below.

Easy

< 1min

Consider the graphs shown below.

Easy

< 1min

We are going to sketch the graph of $y=\log_2x$y=log2x.

Easy

4min

Know simple properties and graphs of the logarithmic function including lnx and graphs of k ln(ax + b) where n, k, a and b are integers.

Know simple properties and graphs of the exponential function including e^x and graphs of ke^(nx) + a where n and k are integers.