Evaluate the logarithmic equation for three values of x that are greater 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. State the equation of the line asymptotic to the graph (if any).
y= log 1/7^x
the way you typed it, it would mean y = 0 , since log1 = 0
if you meant
y = log(1/7^x) then
y = log1 - log7^x
= 0 - xlog7
= -0.8451x which is a straight line
or perhaps did you mean y = (log (1/7))^x ?
- can you see the ambiguity of the question if no brackets are used?
To evaluate the logarithmic equation y = log(1/7^x) for different values of x, we will substitute those values into the equation and calculate the corresponding values of y.
Let's start with three values of x that are greater than 1. Let's choose x = 2, x = 3, and x = 4.
For x = 2:
y = log(1/7^2) = log(1/49) = -1.7 (rounded to one decimal place)
For x = 3:
y = log(1/7^3) = log(1/343) = -2.5 (rounded to one decimal place)
For x = 4:
y = log(1/7^4) = log(1/2401) = -3.4 (rounded to one decimal place)
We will now move on to three values of x that are between 0 and 1. Let's choose x = 0.2, x = 0.5, and x = 0.8.
For x = 0.2:
y = log(1/7^0.2) = log(1/1.378) = 0.140 (rounded to three decimal places)
For x = 0.5:
y = log(1/7^0.5) = log(1/2.646) = 0.397 (rounded to three decimal places)
For x = 0.8:
y = log(1/7^0.8) = log(1/5.265) = 0.623 (rounded to three decimal places)
Finally, let's evaluate the equation at x = 1:
For x = 1:
y = log(1/7^1) = log(1/7) = -0.15 (rounded to two decimal places)
Now, we have the following ordered pairs (x, y):
(2, -1.7)
(3, -2.5)
(4, -3.4)
(0.2, 0.140)
(0.5, 0.397)
(0.8, 0.623)
(1, -0.15)
Plotting these points on a graph, we get:
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The equation y = log(1/7^x) does not have a horizontal asymptote, as the logarithmic function approaches negative infinity as x approaches infinity.