Question 249519: Evaluate the logarithmic equation for three values of x that are less than -1, three values of x that are between 0 and -1, and at x = -1. Show your work. Use the resulting ordered pairs to plot the graph; submit the graph via the Dropbox. State the equation of the line asymptotic to the graph (if any).
y = -log3.5 (-x) The 3.5 is a, or the subscript
Thank you for any help you can offer.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your equation is:
y = -log(3.5,(-x))
graph of this equation looks like this:
you can use the conversion formula to change the base of the logarithm so you can solve it using your calculator.
the conversion formula is:
log(a,(x)) = log(b,x) / log(b,a)
what this formula says is:
log of x to the base of a equals the log of x to the base of b divided by the log of a to the base of b.
in your problem, this conversion formula becomes:
-log(3.5,(-x)) = - (log(10,(-x)) / log(10,3.5)
you can now use your calculator to solve for selected points of that log.
you get:
y = - (log(10,(-x)) / log(10,3.5)
substitute the following values for x:
y = - (log(10,-(-4)) / log(10,3.5) = -1.106589511
y = - (log(10,-(-3)) / log(10,3.5) = -.87695144
y = - (log(10,-(-2)) / log(10,3.5) = -.553294756
y = - (log(10,-(-1)) / log(10,3.5) = -0
y = - (log(10,-(-.1)) / log(10,3.5) = 1.838005394
y = - (log(10,-(-.0000001)) / log(10,3.5) = 12.86603776
the graph appears to be asymptotic at x = 0
the closer you get to 0, the bigger y gets.
the value of y is undefined at x = 0
all you need to do is plot the points on a piece of graph paper and draw the resulting curve.
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