Solve the given equation for $$ x $$. $$ 5^{3 x-6}=40 $$ $$ x=\square $$

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Solve the equation $$ 5^{3x-6}=40 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$5^{3x-6}=40$$
- step1: Take the logarithm of both sides:
  $$\log_{5}{\left(5^{3x-6}\right)}=\log_{5}{\left(40\right)}$$
- step2: Evaluate the logarithm:
  $$3x-6=\log_{5}{\left(40\right)}$$
- step3: Move the constant to the right side:
  $$3x=\log_{5}{\left(40\right)}+6$$
- step4: Divide both sides:
  $$\frac{3x}{3}=\frac{\log_{5}{\left(40\right)}+6}{3}$$
- step5: Divide the numbers:
  $$x=\frac{\log_{5}{\left(40\right)}+6}{3}$$
- step6: Simplify:
  $$x=\frac{7+3\log_{5}{\left(2\right)}}{3}$$
The solution to the equation $$5^{3x-6}=40$$ is $$x=\frac{7+3\log_{5}{(2)}}{3}$$.
$$ x = \frac{7 + 3 \log_{5}(2)}{3} $$

Solve the given equation for .

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