Question

2. Consider the function y = xn (for n = -2). Take the natural logarithm of both sides and plot ln(y) vs. ln(x) on the graph below. Explain or show how to obtain “n” from the graph. (Hint: Can you fit the graph below to a straight line?) (use x=1, 2, 3, 4, 5, 6)

Answer 1

Answer on Question #64923-Physics-Other

Consider the function $y = xn$ (for $n = -2$ ). Take the natural logarithm of both sides and plot $\ln(y)$ vs. $\ln(x)$ on the graph below. Explain or show how to obtain "n" from the graph. (Hint: Can you fit the graph below to a straight line?) (use $x = 1, 2, 3, 4, 5, 6$ )

Solution

$$y = x ^ {n}.$$ $$\ln y = \ln x ^ {n} = n \ln x$$

For $n = -2$ :

$$\ln y = - 2 \ln x$$

It is a straight line.

We can obtain "n" from the graph as the slope of the line:

$$n = \frac {- 4 - (- 2)}{2 - 1} = - 2.$$

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