Question Solve for $$ x: \log _{6} x+\log _{6} x=2 $$ (If there is no solution, enter $$ \varnothing $$ as your answer.)

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Solve the equation $$ \log_{6}x+\log_{6}x=2 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\log_{6}{\left(x\right)}+\log_{6}{\left(x\right)}=2$$
- step1: Find the domain:
  $$\log_{6}{\left(x\right)}+\log_{6}{\left(x\right)}=2,x>0$$
- step2: Add the terms:
  $$2\log_{6}{\left(x\right)}=2$$
- step3: Divide both sides:
  $$\frac{2\log_{6}{\left(x\right)}}{2}=\frac{2}{2}$$
- step4: Divide the numbers:
  $$\log_{6}{\left(x\right)}=1$$
- step5: Convert the logarithm into exponential form:
  $$x=6^{1}$$
- step6: Evaluate the power:
  $$x=6$$
- step7: Check if the solution is in the defined range:
  $$x=6,x>0$$
- step8: Find the intersection:
  $$x=6$$
The solution to the equation $$ \log_{6} x + \log_{6} x = 2 $$ is $$ x = 6 $$.
$$ x = 6 $$.

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