Solve for $$ x $$ in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. $$ 8^{-2 x}=3 $$ $$ x=\square $$

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Solve the equation $$ 8^{-2x}=3 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$8^{-2x}=3$$
- step1: Take the logarithm of both sides:
  $$\log_{8}{\left(8^{-2x}\right)}=\log_{8}{\left(3\right)}$$
- step2: Evaluate the logarithm:
  $$-2x=\log_{8}{\left(3\right)}$$
- step3: Change the signs:
  $$2x=-\log_{8}{\left(3\right)}$$
- step4: Divide both sides:
  $$\frac{2x}{2}=\frac{-\log_{8}{\left(3\right)}}{2}$$
- step5: Divide the numbers:
  $$x=-\frac{\log_{8}{\left(3\right)}}{2}$$
- step6: Simplify:
  $$x=-\frac{\log_{2}{\left(3\right)}}{6}$$
The solution to the equation $$8^{-2x}=3$$ is $$x=-\frac{\log_{2}{(3)}}{6}$$.

To round the answer to the nearest hundredth, we need to calculate the value of $$x$$ and then round it to two decimal places.

Let's calculate the value of $$x$$:
$$x=-\frac{\log_{2}{(3)}}{6}$$

Now, let's round the value of $$x$$ to the nearest hundredth.
Round the number by following steps:
- step0: Round $$-\frac{\log_{2}{(3)}}{6}$$ to $$2$$ decimal places using standard rounding method:
  $$-\frac{\log_{2}{(3)}}{6}$$
- step1: Evaluate:
  $$-\frac{\log_{2}{\left(3\right)}}{6}$$
- step2: Rewrite in decimal:
  $$-0.264160$$
- step3: Round $$-0.264160$$ to $$2$$ decimal places using standard rounding method$$:$$
  $$-0.26$$
The value of $$x$$ rounded to the nearest hundredth is $$-0.26$$.
$$ x \approx -0.26 $$

Solve for in the equation below.
Round your answer to the nearest hundredth.
Do not round any intermediate computations.

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Solve for in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations.