Question

In the following exercises, graph each logarithmic function.

$y={\log }_5\left(x\right)$

Short answer

The graph of the function $y={\log }_5\left(x\right)$is

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 $y={\log }_5\left(x\right)$.

The equivalent exponential function is given as $5^y=x$,

Step 2. Make a table of values

We will use the exponential function $5^y=x$to make a table of values.

$y$	$5^y=x$	$(x,y)$
$-2$	$5^{-2}=\frac{1}{25}$	$(\frac{1}{25},-2)$
$-1$	$5^{-1}=\frac{1}{5}$	$(\frac{1}{5},1)$
$0$	$5^0=1$	$(1,0)$
$1$	$5^1=5$	$(5,1)$
$2$	$5^2=25$	$(25,2)$

Step 3. Draw the graph

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