Question 630539
<pre>
If you have a graphing calculator, I would suggest always drawing the 
graph first.  Here is the graph:

{{{drawing(600,340,-20,10,-4,13,
green(line(-17,-30,-17,30)),
graph(600,340,-20,10,-4,13,4ln(x+17)/ln(3)) ))}}} 

The graph has a vertical asymptote x = -17 (the green line).

Logarithms are only taken of positive numbers.  To get that domain,

set x + 17 > 0
         x > -17

The domain is {x|x > -17} 

In interval notation that's written (-17,{{{infinity}}})

To find the y-intercept:

Set x = 0,

y = {{{ 4log (3, (0+17)) ) }}} 

y={{{ 4log (3, (17)) ) }}} = {{{4log(10,(17))/log(10,(3))}}} = 10.31560769

So the y-intercept is (0, 10.31560769)

To find the x-intercept,

Set y = 0

y = {{{ 4log (3, (x+17)) ) }}} = 0

{{{ 4log (3, (x+17)) ) }}} = 0

Divide both sides by 4

{{{ log (3, (x+17)) ) }}} = 0         

Write the equivalent exponential form of that equation:

x + 17 = 3<sup>0</sup>
x + 17 = 1
     x = -16

So the x-intercept is (-16,0).  As you see all these check with the graph. 

Edwin</pre>