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To expand the logarithm \(\log\left(\frac{t}{7}\right)\), we use the logarithm property for division:

\[
\log\left(\frac{a}{b}\right) = \log(a) - \log(b).
\]

Applying this property to the given expression:

\[
\log\left(\frac{t}{7}\right) = \log(t) - \log(7).
\]

So, the expanded form of \(\log\left(\frac{t}{7}\right)\) is:

\[
\log(t) - \log(7).
\]

Would you like more details on this, or do you have any other questions?

Here are 5 related questions to consider:
1. How would you expand \(\log\left(\frac{xy}{z}\right)\)?
2. What is the expanded form of \(\log\left(x^2y\right)\)?
3. How do you simplify \(\log(100) + \log(0.01)\)?
4. What is the value of \(\log(1)\)?
5. How do the properties of logarithms help in solving equations?

**Tip:** Remember that the properties of logarithms can make complex expressions easier to work with by converting products, quotients, and powers into sums, differences, and multiples.

Expand the logarithm. Assume all expressions exist and are well-defined. Write your answer as a sum or difference of common logarithms or multiples of common logarithms. The inside of each logarithm must be a distinct constant or variable.

Explore the process of expanding the logarithm log(t/7) using the logarithmic property for division. Learn how to simplify expressions into sums or differences of common logarithms, specifically addressing high school level algebra and properties of logarithms.

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