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 April 16th, 2018, 09:49 AM #1 Newbie   Joined: Apr 2018 From: Calgary Posts: 3 Thanks: 0 Solve for x y=a*(1+(b*m*x))^(-1/b) How to solve for x?
 April 16th, 2018, 09:57 AM #2 Senior Member   Joined: May 2016 From: USA Posts: 1,310 Thanks: 550 Why is this in calculus? Here's a start (making certain assumptions on the values of a, b, and m): $y = a(1 + bmx)^{(-1/b)} \implies y = \dfrac{a}{\sqrt[b]{1 + bmx}} \implies$ $\sqrt[b]{1 + bmx} = \dfrac{a}{y} \implies WHAT?$
 April 16th, 2018, 10:13 AM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,145 Thanks: 1003 y / a = 1 / (1 + bmx)^(1 / b) (1 + bmx)^(1 / b) = a / y Can you finish it? We do not give out full solutions.
 April 16th, 2018, 10:26 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,383 Thanks: 2011 Moved from Calculus to Algebra.
 April 16th, 2018, 10:35 AM #5 Newbie   Joined: Apr 2018 From: Calgary Posts: 3 Thanks: 0 ok. thanks
 April 16th, 2018, 11:17 AM #6 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,145 Thanks: 1003 Hint: if x^a = y, then x = y^(1 / a)
 April 16th, 2018, 02:19 PM #7 Newbie   Joined: Apr 2018 From: Calgary Posts: 3 Thanks: 0 x=((((y/a)^(-b))-1)/bm) Did I get it right?
April 16th, 2018, 03:24 PM   #8
Math Team

Joined: Oct 2011

Posts: 14,145
Thanks: 1003

Quote:
 Originally Posted by amirriazahmed x=((((y/a)^(-b))-1)/bm) Did I get it right?
YES...but you need to bracket the denominator bm:
x=((((y/a)^(-b))-1)/(bm))

You have extra brackets (ok to leave as they are but not required);
this is sufficient: x=((y / a)^(-b) - 1) / (bm)

Can be rearranged this way:
x = ((a / y)^b - 1) / (bm)

You can check if correct by using original equation and assigning
values to a,b,m,x then calculating y from these values,
then seeing if x comes out ok using your "solution equation".
Try it; say a=2, b=3, c=4, x=5.
See what I mean?

 April 16th, 2018, 03:27 PM #9 Global Moderator   Joined: Dec 2006 Posts: 20,383 Thanks: 2011 Nearly... x = ((y/a)^(-b) - 1)/(bm) has correct use of parentheses, or you could give x = ((a/y)^b - 1)/(bm).

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