b $$ \quad 3^{x+1}=3^{x-1}+3^{2} $$

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Solve the equation $$ 3^{x+1}=3^{x-1}+3^{2} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$3^{x+1}=3^{x-1}+3^{2}$$
- step1: Evaluate the power:
  $$3^{x+1}=3^{x-1}+9$$
- step2: Move the expression to the left side:
  $$3^{x+1}-3^{x-1}=9$$
- step3: Calculate:
  $$8	imes 3^{x-1}=9$$
- step4: Divide both sides:
  $$\frac{8	imes 3^{x-1}}{8}=\frac{9}{8}$$
- step5: Divide the numbers:
  $$3^{x-1}=\frac{9}{8}$$
- step6: Take the logarithm of both sides:
  $$\log_{3}{\left(3^{x-1}ight)}=\log_{3}{\left(\frac{9}{8}ight)}$$
- step7: Evaluate the logarithm:
  $$x-1=\log_{3}{\left(\frac{9}{8}ight)}$$
- step8: Move the constant to the right side:
  $$x=\log_{3}{\left(\frac{9}{8}ight)}+1$$
- step9: Simplify:
  $$x=3-3\log_{3}{\left(2ight)}$$
The solution to the equation $$3^{x+1}=3^{x-1}+3^{2}$$ is $$x=3-3\log_{3}{(2)}$$.
$$x=3-3\log_{3}{(2)}$$

b

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