Maria wrote the equation $$ \log \left(\frac{x}{2}\right)+\log \left(\frac{20}{x^{2}}\right)=\log 8 $$. What is the solution to Maria's equation? $$ x=\frac{3}{10} $$ $$ x=\frac{4}{5} $$ $$ x=\frac{5}{4} $$ $$ x=\frac{10}{2} $$

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Solve the equation $$ \log \left(\frac{x}{2}ight)+\log \left(\frac{20}{x^{2}}ight)=\log 8 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\log_{10}{\left(\frac{x}{2}ight)}+\log_{10}{\left(\frac{20}{x^{2}}ight)}=\log_{10}{\left(8ight)}$$
- step1: Find the domain:
  $$\log_{10}{\left(\frac{x}{2}ight)}+\log_{10}{\left(\frac{20}{x^{2}}ight)}=\log_{10}{\left(8ight)},x>0$$
- step2: Add the terms:
  $$\log_{10}{\left(\frac{10}{x}ight)}=\log_{10}{\left(8ight)}$$
- step3: Evaluate the logarithm:
  $$\frac{10}{x}=8$$
- step4: Cross multiply:
  $$10=x	imes 8$$
- step5: Simplify the equation:
  $$10=8x$$
- step6: Rewrite the expression:
  $$2	imes 5=2	imes 4x$$
- step7: Evaluate:
  $$5=4x$$
- step8: Swap the sides:
  $$4x=5$$
- step9: Divide both sides:
  $$\frac{4x}{4}=\frac{5}{4}$$
- step10: Divide the numbers:
  $$x=\frac{5}{4}$$
- step11: Check if the solution is in the defined range:
  $$x=\frac{5}{4},x>0$$
- step12: Find the intersection:
  $$x=\frac{5}{4}$$
The solution to Maria's equation is $$ x = \frac{5}{4} $$ or $$ x = 1.25 $$.

Therefore, the correct answer is $$ x = \frac{5}{4} $$.
The solution is $$ x = \frac{5}{4} $$.

Maria wrote the equation . What is the solution to Maria’s equation?

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