log 4 (x) = sqrt(log 4 (x))    find x values

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log 4 (x) = sqrt(log 4 (x))

Let us square both sides :

==> (log 4 (x))^2 = log 4 (x)

Now move log 4 (x) to the left side:

==>( log 4 (x))^2 - log 4 (x) = 0

Now factor log 4 (x):

==> log 4 (x) [...

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log 4 (x) = sqrt(log 4 (x))

Let us square both sides :

==> (log 4 (x))^2 = log 4 (x)

Now move log 4 (x) to the left side:

==>( log 4 (x))^2 - log 4 (x) = 0

Now factor log 4 (x):

==> log 4 (x) [ (log 4 (x)) -1 ] =0

==> log 4 (x) = 0 ==> x1 = 1

and log 4 (x) -1 = 0 ==> log 4 (x) = 1 ==> x2 = 4

Then x = {1,4}

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