The first step is to eliminate the square root, and for
this reason, we'll raise to square, both sides of the
equation:
[log 4 (x)]^2 = [sqrt(log 4
(x))]^2
[log 4 (x)]^2 = log 4
(x)
We'll subtract log 4 (x) both
sides:
[log 4 (x)]^2 - log 4 (x) =
0
We'll use the substitution technique to solve the
equation:
log 4 (x) = t
t^2 -
t = 0
We'll factorize:
t(t-1)
= 0
t1 = 0
t-1 =
0
t2 = 1
log 4 (x) =
0
x = 4^0
x =
1
log 4 (x) = 1
x =
4^1
x = 4
The
solutions of the equation are: x1 = 1 and x2 = 4.
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