Solve for x if log (x^2) - log 2x = 2.

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log (x^2) - log 2x = 2

We will use the logarithm properties to solve for x.

First, we know that log a - log b = log (a/b)

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

Now we will substitute into the equation.

==> log (x/2) = 2

Now we will use the exponent form to rewrite the equation.

==> (x/2) = 10^2

==> x/2 = 100

Now we will multiply by 2.

==> x = 200

Then the answer for the equation is x= 200

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