Solve $$ 5^{x+1}=4 $$ for $$ x $$. Find the exact solution.

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Solve the equation $$ 5^{x+1}=4 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$5^{x+1}=4$$
- step1: Take the logarithm of both sides:
  $$\log_{5}{\left(5^{x+1}\right)}=\log_{5}{\left(4\right)}$$
- step2: Evaluate the logarithm:
  $$x+1=\log_{5}{\left(4\right)}$$
- step3: Move the constant to the right side:
  $$x=\log_{5}{\left(4\right)}-1$$
- step4: Simplify:
  $$x=2\log_{5}{\left(2\right)}-1$$
The exact solution to the equation $$5^{x+1}=4$$ for $$x$$ is $$x=2\log_{5}(2)-1$$.
The exact solution is $$ x = 2\log_{5}(2) - 1 $$.

Solve for . Find the exact solution.

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