Find the solution to the equation, $$ 3+2 \ln \left(\frac{x}{7}+3\right)=-4 $$ (correct to 4 decimal places) $$ \} x=\square $$

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Solve the equation $$ 3+2 \ln \left(\frac{x}{7}+3ight)=-4 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$3+2\ln{\left(\frac{x}{7}+3ight)}=-4$$
- step1: Find the domain:
  $$3+2\ln{\left(\frac{x}{7}+3ight)}=-4,x>-21$$
- step2: Move the expression to the left side:
  $$3+2\ln{\left(\frac{x}{7}+3ight)}-\left(-4ight)=0$$
- step3: Subtract the numbers:
  $$7+2\ln{\left(\frac{x}{7}+3ight)}=0$$
- step4: Rewrite the expression:
  $$2\ln{\left(\frac{x}{7}+3ight)}=-7$$
- step5: Divide both sides:
  $$\frac{2\ln{\left(\frac{x}{7}+3ight)}}{2}=\frac{-7}{2}$$
- step6: Divide the numbers:
  $$\ln{\left(\frac{x}{7}+3ight)}=-\frac{7}{2}$$
- step7: Convert the logarithm into exponential form:
  $$\frac{x}{7}+3=e^{-\frac{7}{2}}$$
- step8: Evaluate the power:
  $$\frac{x}{7}+3=\frac{e^{\frac{1}{2}}}{e^{4}}$$
- step9: Add or subtract both sides:
  $$\frac{x}{7}=\frac{e^{\frac{1}{2}}}{e^{4}}-3$$
- step10: Calculate:
  $$\frac{x}{7}=\frac{e^{\frac{1}{2}}-3e^{4}}{e^{4}}$$
- step11: Rewrite the expression:
  $$\frac{x}{7}=\frac{\sqrt{e}-3e^{4}}{e^{4}}$$
- step12: Multiply both sides of the equation by $$7:$$
  $$\frac{x}{7}	imes 7=\frac{\sqrt{e}-3e^{4}}{e^{4}}	imes 7$$
- step13: Multiply the terms:
  $$x=\frac{\left(\sqrt{e}-3e^{4}ight)	imes 7}{e^{4}}$$
- step14: Divide the terms:
  $$x=\frac{7\sqrt{e}-21e^{4}}{e^{4}}$$
- step15: Check if the solution is in the defined range:
  $$x=\frac{7\sqrt{e}-21e^{4}}{e^{4}},x>-21$$
- step16: Find the intersection:
  $$x=\frac{7\sqrt{e}-21e^{4}}{e^{4}}$$
The solution to the equation $$3+2 \ln \left(\frac{x}{7}+3ight)=-4$$ is $$x \approx -20.7886$$ (correct to 4 decimal places).
$$ x \approx -20.7886 $$

Find the solution to the equation,
(correct to 4 decimal places)

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Find the solution to the equation, (correct to 4 decimal places)