SOLUTION: I can't find any examples of logarithmic functions that have another number before the logarithm. I have to find the domain, x-intercept, and y-intercept for the following problem:

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I can't find any examples of logarithmic functions that have another number before the logarithm. I have to find the domain, x-intercept, and y-intercept for the following problem:      Log On


   

Question 630539: I can't find any examples of logarithmic functions that have another number before the logarithm. I have to find the domain, x-intercept, and y-intercept for the following problem:
y=+4log+%283%2C+%28x%2B17%29%29+%29+
So far I have domain: x>17 y-intercept: (0,-16) and I can't find x-intercept.
Are these right, and how do I work out the x-intercept?
Thanks :)
Found 2 solutions by ewatrrr, Edwin McCravy:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

y=+4%2Alog+%283%2C+%28x%2B17%29%29+%29 Note: Domain of +4%2Alog+%283%2C+%28x%2B17%29%29+%29 is the same as the domain of =log+%283%2C+%28x%2B17%29%29+%29

 x-intercept is when y = 0, it is (-16,0)  3^0 = 1 = x+17, x+=+-16

 y-intercept is when x = 0

   y =  = log 17^4/log 3  || log  base ten

Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!
If you have a graphing calculator, I would suggest always drawing the 
graph first.  Here is the graph:

 

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+%283%2C+%280%2B17%29%29+%29+ 

y=+4log+%283%2C+%2817%29%29+%29+ = 4log%2810%2C%2817%29%29%2Flog%2810%2C%283%29%29 = 10.31560769

So the y-intercept is (0, 10.31560769)

To find the x-intercept,

Set y = 0

y = +4log+%283%2C+%28x%2B17%29%29+%29+ = 0

+4log+%283%2C+%28x%2B17%29%29+%29+ = 0

Divide both sides by 4

+log+%283%2C+%28x%2B17%29%29+%29+ = 0         

Write the equivalent exponential form of that equation:

x + 17 = 30
x + 17 = 1
     x = -16

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

Edwin