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The expression you've uploaded is:

\[
\log_{\sqrt{6}} 216
\]

To solve this, we can use the change of base formula and simplify. Let's proceed step-by-step.

1. **Rewrite the base**: We know that \(\sqrt{6} = 6^{1/2}\), so we can rewrite the expression as:
   \[
   \log_{6^{1/2}} 216
   \]

2. **Use the Power Rule for Logarithms**: The logarithmic identity \(\log_{a^b} x = \frac{\log_a x}{b}\) applies here. Thus, we can rewrite this as:
   \[
   \frac{\log_6 216}{1/2} = 2 \cdot \log_6 216
   \]

3. **Evaluate \(\log_6 216\)**: We need to determine the value of \(\log_6 216\). If we assume \(216 = 6^x\), we find \(x\) by solving the equation. However, \(216\) is not an integer power of \(6\), so we would likely need a calculator to approximate this logarithm in terms of base \(10\) or base \(e\).

Would you like me to continue with an approximation, or are you interested in additional details? 

---

1. How do you convert between logarithmic bases in general?
2. What is the power rule for logarithms and when is it useful?
3. Why might approximations be necessary for non-integer powers in logarithmic calculations?
4. How can logarithmic identities simplify complex expressions?
5. How does understanding fractional exponents help in evaluating logarithmic expressions?

**Tip:** When dealing with unusual bases, rewriting in terms of simpler expressions can make calculations easier.

Explore how to solve the logarithmic expression log_√6 (216) by applying the change of base formula and power rule. This problem covers key logarithmic identities, ideal for high school students in Grades 10-12.

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