Question

In the following exercises, graph each logarithmic function.

$y={\log }_{0.8}\left(x\right)$

Short answer

The graph of the function $y={\log }_{0.8}\left(x\right)$is given as

Step-by-step solution

Step 1. Convert into exponential function  

To graph a logarithmic function, it is easiest to convert the equation to its exponential form,

Consider the logarithmic function $y={\log }_{0.8}\left(x\right)$.

The equivalent exponential function is given as $0.8^y=x$.

Step 2. Make a table of values  

We will use the exponential function $0.8^y=x$to make a table of values.

$y$	$0.8^y=x$	$(x,y)$
$-2$	$0.8^{-2}=1.5625$	$(1.5625,-2)$
$-1$	$0.8^{-1}=1.25$	$(1.25,-1)$
$0$	$0.8^0=1$	$(1,0)$
$1$	$0.8^1=0.8$	role="math" localid="1645084040109" $(0.8,1)$
$2$	$0.8^2=0.64$	$(0.64,2)$

Step 3. Draw the graph 

Using the table of values the graph of the function is given as