Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation; and 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 of each function; submit the graphs via the Dropbox. y=5^(x-2),x=5^(y-2)

What is your question about this? SEntence one is straightforward. Use your calculator.

Sentence two:
lny=(x-2)ln5, evaluate for given x,find y.

To evaluate the exponential equation y = 5^(x-2) for various values of x, we simply substitute those values into the equation. Let's start with three positive values of x:

1. For x = 1: y = 5^(1-2) = 5^(-1) = 1/5
2. For x = 2: y = 5^(2-2) = 5^0 = 1
3. For x = 3: y = 5^(3-2) = 5^1 = 5

Now, let's evaluate the equation for three negative values of x:

1. For x = -1: y = 5^(-1-2) = 5^(-3) = 1/125
2. For x = -2: y = 5^(-2-2) = 5^(-4) = 1/625
3. For x = -3: y = 5^(-3-2) = 5^(-5) = 1/3125

Finally, let's evaluate the exponential equation for x = 0:

For x = 0: y = 5^(0-2) = 5^(-2) = 1/25

To transform the second expression, x = 5^(y-2), to the equivalent logarithmic equation, we rewrite it as log base 5 (x) = y - 2.

Now, let's evaluate the logarithmic equation for three values of x that are greater than 1:

1. For x = 5: log base 5 (5) = y - 2
y - 2 = 1 --> y = 3

2. For x = 25: log base 5 (25) = y - 2
y - 2 = 2 --> y = 4

3. For x = 125: log base 5 (125) = y - 2
y - 2 = 3 --> y = 5

Next, let's evaluate the logarithmic equation for three values of x between 0 and 1:

1. For x = 1/5: log base 5 (1/5) = y - 2
y - 2 = -1 --> y = 1

2. For x = 1/25: log base 5 (1/25) = y - 2
y - 2 = -2 --> y = 0

3. For x = 1/125: log base 5 (1/125) = y - 2
y - 2 = -3 --> y = -1

Finally, let's evaluate the logarithmic equation for x = 1:

For x = 1: log base 5 (1) = y - 2
y - 2 = 0 --> y = 2

Now, we have the following ordered pairs for the exponential equation: (1, 1/5), (2, 1), (3, 5), (-1, 1/125), (-2, 1/625), (-3, 1/3125), (0, 1/25). And for the logarithmic equation: (5, 3), (25, 4), (125, 5), (1/5, 1), (1/25, 0), (1/125, -1), (1, 2).

You can use these ordered pairs to plot the graphs of each function.