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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