To express $\log \left( \frac{5a}{11} \right)$ as the sum and/or difference of logarithms, we can use the properties of logarithms:

1. Quotient Rule: $\log \left( \frac{A}{B} \right) = \log A - \log B$
2. Product Rule: $\log (A \cdot B) = \log A + \log B$

Using these properties, we get:

$\log \left( \frac{5a}{11} \right) = \log(5a) - \log(11)$

Next, we apply the product rule to $\log(5a)$:

$\log(5a) = \log(5) + \log(a)$

Putting it all together:

$\log \left( \frac{5a}{11} \right) = \log(5) + \log(a) - \log(11)$

Thus, the expression as the sum and/or difference of logarithms is:

$\log(5) + \log(a) - \log(11)$

Would you like more details on any step, or have any questions?

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Here are 5 related questions to deepen your understanding:

1. How would you simplify $\log \left( \frac{7x^2}{3y} \right)$?
2. What is the expanded form of $\log \left( \frac{a^3b}{c} \right)$?
3. How can you express $\log \left( \frac{mn}{p^2} \right)$ as a sum and/or difference of logarithms?
4. If given $\log(3a) + \log(4b)$, how could you combine it into a single logarithm?
5. What would $\log(a^5b^2) - \log(c^3)$ simplify to?

Tip: Remember to apply the product, quotient, and power rules step-by-step for clarity when expanding or simplifying logarithmic expressions.