Question 975006: A power function with form y= a x^p passes through the points (3, 2/81) and (6, 1/1296). Find the constants a and p
*last one that I'm stuck on, I was able to get a=6 but I'm just lousy with fractions so I don't know how to get ^p.
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website! "Lousy at fractions" is something that needs to be fixed before trying to study intermediate algebra or the topic of exponential and logarithmic equations.
Attempt at linearizing your given equation should be tried.
This last one being a linear equation in  , as a variable, slope of p, vertical axis intercept  . The ordered pair points are as ( ln(x), ln(y) ). Your given points must be adjusted for the format of your linearized equation and points.
Your data points to be on your line must be ( ln(3), ln(2/81) ) and ( ln(6), ln(1/1296) ).
I chose natural log only because typing in pure text is less trouble that way. You can instead use any reasonable base you want, such as the other popular base, 10.
calculate your two points, use whatever method you need to determine vertical axis intercept and slope. Finish making your specific, given equation.
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