Question

In the following exercises, solve each logarithmic equation$y={\log }_{0.4}x$

Short answer

The graph is

Step-by-step solution

Given information

Given function$y={\log }_{0.4}x$

Rewriting in exponential form

Rewriting, we get

${(0.4)}^y=x$

Using the point plotting method

Using the point plotting, we get

$y$	${(0.4)}^y=x$	$(x,y)$
$0$	$1$	$(1,0)$
$-1$	$\frac{5}{2}$	$(\frac{5}{2},-1)$
$1$	$0.4$	$(0.4,1)$

Sketching the graph using plotting the points

Sketching, we get