solve for x : 4^x -( 2^ x+1) -8 = 0

Question

Solve for x in this equition 

 

4^x - (2^ x+1) -8 = 0

Answer 1

I am assuming that the equation is 4^x - 2^x+1 - 8 = 0

 

4^x - 2(2^x) - 8 = 0

 

(2^x)² - 2(2^x) - 8 = 0

 

Let u = 2^x.  Then the equation becomes u² - 2u - 8 = 0

 

                                                        (u - 4)(u + 2) = 0

 

                                                        u = 4 or u = -2

 

So, 2^x = 4 or 2^x = -2

 

Since 2^x is positive for all x, we can disregard the equation 2^x = -2.

 

Therefore, 2^x = 4

 

               2^x = 2²     x = 2