Solve ` 2 log_(3) x - 4 log_(x) 27 le 5`.

Explanation

To solve the inequality \( 2 \log_{3} x - 4 \log_{x} 27 \leq 5 \), we will follow these steps:

### Step 1: Rewrite the logarithm
We can use the change of base formula for logarithms. Recall that \( \log_{a} b = \frac{1}{\log_{b} a} \). Thus, we can rewrite \( \log_{x} 27 \) as \( \frac{1}{\log_{27} x} \).

So, we have:
\[
2 \log_{3} x - 4 \cdot \frac{1}{\log_{27} x} \leq 5
...