log 2 (2x) + log 4 (4x^2) = 3

First let us rewrite :

We know that:

log a b = log c b/log c a

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

But log 2 4 = 2

==> log 4 (4x^2) =(1/2) log 2 (4x^2) = log 2 (4x^2)^1/2

==> log 2 (2x) + log 2 (4x^2)^1/2 = 3

==> log 2 (2x) + log 2 (2x) = 3

We know thatL log a + log b = log a*b

==> log 2 (2x)*(2x) = 3

==> log 2 (4x^2) = 3

==> 4x^2 = 2^3

==> 4x^2 = 8

==> x^2 = 2

==> **x = sqrt2**

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