If $$ \ln (7 x+5)=2 $$, then $$ x=\square $$

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Solve the equation $$ \ln(7x+5)=2 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\ln{\left(7x+5\right)}=2$$
- step1: Find the domain:
  $$\ln{\left(7x+5\right)}=2,x>-\frac{5}{7}$$
- step2: Convert the logarithm into exponential form:
  $$7x+5=e^{2}$$
- step3: Move the constant to the right side:
  $$7x=e^{2}-5$$
- step4: Divide both sides:
  $$\frac{7x}{7}=\frac{e^{2}-5}{7}$$
- step5: Divide the numbers:
  $$x=\frac{e^{2}-5}{7}$$
- step6: Check if the solution is in the defined range:
  $$x=\frac{e^{2}-5}{7},x>-\frac{5}{7}$$
- step7: Find the intersection:
  $$x=\frac{e^{2}-5}{7}$$
The solution to the equation $$ \ln(7x+5)=2 $$ is $$ x = \frac{e^{2}-5}{7} $$.
$$ x = \frac{e^{2}-5}{7} $$

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