Write the following as the sum and/or difference of logarithms. Assume all variables are positive.

log(5a/11)=

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.

Write the following as the sum and/or difference of logarithms. Assume all variables are positive.

log(5a/11) =

Explore how to express log(5a/11) as the sum and/or difference of logarithms by applying the properties of logarithms. This step-by-step solution demonstrates the use of the quotient and product rules for logarithms, suitable for students in Grades 10-12.

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