To rewrite the logarithm \(\log((17a) \times (2b))\) as a sum, you can apply the logarithm property that states:

\[
\log(m \times n) = \log(m) + \log(n)
\]

Applying this property step by step:

1. First, apply the property to the product inside the logarithm:

\[
\log((17a) \times (2b)) = \log(17a) + \log(2b)
\]

2. Then, apply the same property to each term:

\[
\log(17a) = \log(17) + \log(a)
\]
\[
\log(2b) = \log(2) + \log(b)
\]

3. Combine all the terms together:

\[
\log((17a) \times (2b)) = \log(17) + \log(a) + \log(2) + \log(b)
\]

So, the expression \(\log((17a) \times (2b))\) rewritten as a sum is:

\[
\log(17) + \log(a) + \log(2) + \log(b)
\]

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you rewrite \(\log(\frac{a}{b})\) as a difference?
2. Can you simplify \(\log(100)\) without using a calculator?
3. What is the logarithmic property for \(\log(a^n)\)?
4. How do you combine \(\log(2) + \log(3)\) into a single logarithm?
5. What is the value of \(\log(1)\) and why?

**Tip:** Remember that logarithms turn multiplication into addition and division into subtraction, which is helpful in simplifying complex expressions.

Learn how to rewrite \( \log((17a) \times (2b)) \) as a sum of logarithmic terms step-by-step. This problem involves applying logarithm properties to simplify complex expressions involving products of variables.

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