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:
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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=
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) (Show Source):
Hi,
y= Note: Domain of is the same as the domain of = x-intercept is when y = 0, it is (-16,0) 3^0 = 1 = x+17, y-intercept is when x = 0
y = = log 17^4/log 3 || log base ten
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,)
To find the y-intercept:
Set x = 0,
y =
y= = = 10.31560769
So the y-intercept is (0, 10.31560769)
To find the x-intercept,
Set y = 0
y = = 0
= 0
Divide both sides by 4
= 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