# Lab Exercise: How do I make a logarithmic curve linear?

by CarbonWater
Tags: curve, exercise, linear, logarithmic
 P: 20 1. The problem statement, all variables and given/known data In a certain experiment, the power (P) radiated by a light bulb filament was measured as a function of the filament's absolute temperature (T). Data: P(W) 0.45 0.95 1.8 3.5 5.6 T(K) 1000 1200 1500 1800 2000 (a) Plot the data (Done) (b) Assume a power function and re-plot the data. 2. Relevant equations Unsure. 3. The attempt at a solution I plotted the data and it looks like a natural logarithm. I'm not sure what to do next. Raising each T value to the power of 2 straightens out the curve a bit but not completely. Is that what it means to assume a power function? If a power function is y=kx^a, how do I know which exact a to take and where do I get k from? Thanks.
 HW Helper PF Gold P: 3,394 Suppose P = T^n. Then ln(P) = ln(T^n) = n*ln(T). If you graph your data as ln(P) vs ln(T), (and the data is perfect) you will get a straight line with slope n. Imperfect data (isn't it always?), the slope of a trend line is the best value for n.
 P: 20 Thank you. That was what my professor was looking for.

 Related Discussions General Engineering 25 Biology 8 Calculus & Beyond Homework 5 General Math 4 General Discussion 31