Find all solutions of the equation below. 2log(x+2)=log(2x+4) Select the correct choice below and fill in any answer box(es) to complete your choice. (Simplify your answer. Use a comma to separate answers as needed. Round to four decimal places as needed.) A. There is no solution that is not extraneous. The solution(s) that is/are extraneous is/are x=square B. The solution(s) that is/are not extraneous is/are x=square There is no solution that is extraneous. C. The solution(s) that is/are not extraneous is/are x= The solution(s) that is/are extraneous is/are x=square

## Step1: {Identify the equation}<br />The given equation is $2log(x+2)=log(2x+4)$.<br /><br />## Step2: {Apply logarithm properties}<br />Using the logarithm property $log_b(m^n) = nlog_b(m)$, the equation can be rewritten as $log((x+2)^2)=log(2x+4)$.<br /><br />## Step3: {Solve for x}<br />Since the logarithms on both sides of the equation have the same base and are equal, the arguments must also be equal. Therefore, $(x+2)^2=2x+4$.<br /><br />## Step4: {Simplify the equation}<br />Expanding and simplifying the equation gives $x^2+4x+4=2x+4$. Rearranging the terms gives $x^2+2x=0$.<br /><br />## Step5: {Factor the equation}<br />Factoring the equation gives $x(x+2)=0$.<br /><br />## Step6: {Find the roots}<br />Setting each factor equal to zero gives the solutions $x=0$ and $x=-2$.<br /><br />## Step7: {Check for extraneous solutions}<br />Substituting $x=0$ and $x=-2$ back into the original equation, it is found that $x=-2$ is an extraneous solution because it results in taking the logarithm of a non-positive number, which is undefined. Therefore, the only valid solution is $x=0$.