I forgot how to solve for an exponent

[bocobuff]

Homework Statement

i need to solve for b in f(x)=a*x^b
i know f(1.5)=10 and f(1.7)=14

it's been forever since i did calc like this and i am blank on what to do.
i can't remember if or how i can set them equal to each other to solve for b.
i know i have 2 eqns and 2 unknowns.

do i set f(1.5)=f(1.7)? i don't think that's right but i can't think of what else to do??

 

[NoMoreExams]

Homework Statement

i need to solve for b in f(x)=a*x^b
i know f(1.5)=10 and f(1.7)=14

it's been forever since i did calc like this and i am blank on what to do.
i can't remember if or how i can set them equal to each other to solve for b.
i know i have 2 eqns and 2 unknowns.

do i set f(1.5)=f(1.7)? i don't think that's right but i can't think of what else to do??

Why would you set them equal to each other? You know they equal 10 and 14 respectively so are you saying 10 = 14?

What you should do is plug it in, i.e. f(1.5) = a*1.5^b = 10 then do the same with the other point, now you will have 2 equations and 2 unknowns, so for example a = 10/1.5^b, figure out what a = in the other equation and set THOSE equal to each other.

 

[bocobuff]

alright I'm an idiot.
so you get something like 14/10=(1.7/1.5)^b and then take natural log of each side right...?

 

[NoMoreExams]

Assuming your algebra is correct, yes.

 

[bocobuff]

sweet thanks a lot