SOLUTION: If 4^x+2(2^x)=80 what is the value of x?

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Question 1104176: If 4^x+2(2^x)=80 what is the value of x?
Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.
4%5Ex+%2B+2%282%5Ex%29 = 80 

Introduce new variable u = 2%5Ex.  Then your original equation becomes this quadratic equation

u%5E2+%2B+2u+-+80 = 0.


To solve, factor left side

(u-8)*(u+10) = 0.


It has the roots  u = 8  and  u = -10.


So, according our substitution,

   2%5Ex = 8  with the solution x = 3,

or

   2%5Ex = -10,  which has no solutions.


Answer.  The solution is x = 3.