log 2 x - log 4 x = 2    find x

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log 2 x - log 4 x = 2

Let us rewirte:

We know that:

log a b = log c b/ log c a

==> log 4 x = log 2 x/ log 2 4

                    = log 2 x / 2

                   = (1/2)*log 2 x

==> log 2 x - (1/2) log 2 (x) = 2

==> (1/2) log 2 (x) = 2

No multiply by 2:

==> log 2 (x) = 4

==> x= 2^4

==> x= 16

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