SOLUTION: y=1/5 log(base3)(9x-36)^(15) - 13 Apply the laws of logarithms to change the form of the equation. Graph the function by first stating the basic function and then describe each tr

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: y=1/5 log(base3)(9x-36)^(15) - 13 Apply the laws of logarithms to change the form of the equation. Graph the function by first stating the basic function and then describe each tr      Log On


   

Question 724595: y=1/5 log(base3)(9x-36)^(15) - 13
Apply the laws of logarithms to change the form of the equation. Graph the function by first stating the basic function and then describe each transformation applied in order. Specifically describe what happens to the domain, range, asymptotes, x-intercept, and vertical stretch or compression.
I have a problem with this. What i have tried already:
y= -7 -3log(base3)(x-4)
Found 2 solutions by stanbon, jsmallt9:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
y=1/5 log(base3)(9x-36)^(15) - 13
Apply the laws of logarithms to change the form of the equation.
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y = log3(9x-36)^3 - 13
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Graph the function by first stating the basic function and then describe each transformation applied in order. Specifically describe what happens to the domain, range, asymptotes, x-intercept, and vertical stretch or compression.
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Before Transformation:
y = log3(x)
Domain: x > 0
Range: All Real Numbers
Asymp: x = 0
x-int: log3(x) = 0
x = 3*0 = 1
-----
stretch or compress: none
------------------------------
After Transformation::
Domain: x > 4
Range: All Real Numbers
Asymp: x = 4
x-int: Let y = 0 ; solve for "x"
(9x-36)^3 = 3^13
9x-36 = 3^(13/3) = 116.82
9x = 152.82
x = 16.98
Stretch: Around 30
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cheers,
Stan H.

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
You've done some good work so far but I believe there is an error:
y=%281%2F5%29log%283%2C+%28%289x-36%29%5E%2815%29%29%29+-+13
y=15%2A%281%2F5%29log%283%2C+%289x-36%29%29+-+13
y=3log%283%2C+%289x-36%29%29+-+13
y=3log%283%2C+%289%28x-4%29%29%29+-+13
y=3%28log%283%2C+%289%29%29+%2B+log%283%2C+%28x-4%29%29%29+-+13
y=3%282+%2B+log%283%2C+%28x-4%29%29%29+-+13
y=6+%2B+3log%283%2C+%28x-4%29%29+-+13
y=-7+%2B+3log%283%2C+%28x-4%29%29
Unless I've made an error, there should be a +3 in front of the log.

The basic function is y+=+log%283%2C+%28x%29%29 and its graph looks like:
graph%28400%2C+400%2C+-1%2C+7%2C+-4%2C+4%2C+%281%2Fln%283%29%29%2Aln%28x%29%29
We can see that the domain is all positive numbers (x > 0) and that the range is all real numbers. There is a vertical asymptote at x = 0. The x-intercept is (1, 0).

For y=-7+%2B+3log%283%2C+%28x-4%29%29...
  • The "4" in x-4 will cause a horizontal translation/shift of 4 units to the right.
  • The "3" in front of the log will cause a vertical stretch by a factor of 3.
  • The -7 will cause a vertical translation/shift of 7 units downward.
  • The horizontal shift will shift all x values to the right. So the vertical asymptote and the domain will also be affected in the same way. The new asymptote will be x = 4 and the new domain is x > 4.
  • The range of the base function is all real numbers. Vertically shifting and/or stretching all real numbers will not change the range. The range is still all real numbers.
  • The new x-intercept is not easily predicted with these transformations. We just have to solve:
    0=-7+%2B+3log%283%2C+%28x-4%29%29
    7+=+3log%283%2C+%28x-4%29%29
    7%2F3+=+log%283%2C+%28x-4%29%29
    3%5E%287%2F3%29+=+x+-+4
    4+%2B+3%5E%287%2F3%29+=+x
Here's the graph:
graph%28400%2C+400%2C+-1%2C+19%2C+-15%2C+5%2C+-7+%2B+3%2A%28ln%28x-4%29%2Fln%283%29%29%29

P.S. In response to the question in your "thank you"...
As you've suspected the "3" in x-3 causes a right shift of three. Both the domain and the asymptote move to the right by 3. The "2" in -2 causes a vertical stretch by factor of 2. The "-" in -2 causes a reflection in the x-axis. (Think of the graphs above being flipped upside down.) And the -1 is a vertical shift of -1. The range is still all real numbers. To see some y's that are greater than -1, try some x's between 3 and 4.