Solve for $$ t $$ $$ \log _{9}(9 t+4)-\log _{9} t=\log _{9} 10 $$ $$ t=\square $$

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Solve the equation $$ \log_{9}(9t+4)-\log_{9}t=\log_{9}10 $$.
Solve the equation by following steps:
- step0: Solve for $$t$$:
  $$\log_{9}{\left(9t+4ight)}-\log_{9}{\left(tight)}=\log_{9}{\left(10ight)}$$
- step1: Find the domain:
  $$\log_{9}{\left(9t+4ight)}-\log_{9}{\left(tight)}=\log_{9}{\left(10ight)},t>0$$
- step2: Transform the expression:
  $$\log_{9}{\left(\frac{9t+4}{t}ight)}=\log_{9}{\left(10ight)}$$
- step3: Evaluate the logarithm:
  $$\frac{9t+4}{t}=10$$
- step4: Cross multiply:
  $$9t+4=t	imes 10$$
- step5: Simplify the equation:
  $$9t+4=10t$$
- step6: Move the variable to the left side:
  $$9t+4-10t=0$$
- step7: Subtract the terms:
  $$-t+4=0$$
- step8: Move the constant to the right side:
  $$-t=0-4$$
- step9: Remove 0:
  $$-t=-4$$
- step10: Change the signs:
  $$t=4$$
- step11: Check if the solution is in the defined range:
  $$t=4,t>0$$
- step12: Find the intersection:
  $$t=4$$
The solution to the equation $$\log_{9}(9t+4)-\log_{9}t=\log_{9}10$$ is $$t=4$$.
$$ t=4 $$.

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