Solve for $$ x $$ $$ 2^{x+2}=5^{3 x} $$ Write the exact answer using either base- 10 or base-e logarithms.

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Solve the equation $$ 2^{x+2}=5^{3x} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$2^{x+2}=5^{3x}$$
- step1: Take the logarithm of both sides:
  $$\log_{2}{\left(2^{x+2}ight)}=\log_{2}{\left(5^{3x}ight)}$$
- step2: Evaluate the logarithm:
  $$x+2=3x\log_{2}{\left(5ight)}$$
- step3: Calculate:
  $$x+2=3\log_{2}{\left(5ight)}	imes x$$
- step4: Move the variable to the left side:
  $$x+2-3\log_{2}{\left(5ight)}	imes x=0$$
- step5: Collect like terms:
  $$\left(1-3\log_{2}{\left(5ight)}ight)x+2=0$$
- step6: Move the constant to the right side:
  $$\left(1-3\log_{2}{\left(5ight)}ight)x=0-2$$
- step7: Remove 0:
  $$\left(1-3\log_{2}{\left(5ight)}ight)x=-2$$
- step8: Divide both sides:
  $$\frac{\left(1-3\log_{2}{\left(5ight)}ight)x}{1-3\log_{2}{\left(5ight)}}=\frac{-2}{1-3\log_{2}{\left(5ight)}}$$
- step9: Divide the numbers:
  $$x=-\frac{2}{1-3\log_{2}{\left(5ight)}}$$
The solution to the equation $$2^{x+2}=5^{3x}$$ is $$x=-\frac{2}{1-3\log_{2}{(5)}}$$.
$$ x = -\frac{2}{1 - 3\log_{2}{5}} $$

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Write the exact answer using either base- 10 or base-e logarithms.

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