Monday, January 17, 2011

Solve the equation 4^4x-2*16^x+1=0

This is an exponential equation that
requires substitution technique.


Now, we
notice that 16  = 4^2


We'll re-write the equation
as:


4^4x - 2*4^2x + 1 = 0


It
is a bi-quadratic equation:


We'll substitute 4^2x by
another variable.


4^2x =
a


We'll square raise both
sides:


4^4x  =a^2


 We'll
re-write the equation, having "a" as variable.


a^2 - 2a + 1
= 0


The equation above is the result of expanding the
square:


(a-1)^2 = 0


a1 = a2 =
1


But 4^2x = a1.


4^2x =
1


We'll write 1 as a power of
4:


4^2x = 4^0


Since the bases
are matching, we'll apply the one to one property:


2x =
0


We'll divide by 2:


x =
0.


The solution of the equation is x =
0.

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