Sure, let's transform the given logarithmic expression [tex]\(\log 9 - 2 \log k\)[/tex] into a single logarithm with coefficient 1.
### Step-by-Step Solution
1. Identify the logarithms and their coefficients:
- The first part of the expression is [tex]\(\log 9\)[/tex].
- The second part is [tex]\(-2 \log k\)[/tex].
2. Use the properties of logarithms:
- Recall that [tex]\(a \log b = \log b^a\)[/tex].
- Therefore, [tex]\(-2 \log k\)[/tex] can be rewritten using this property:
[tex]\[
-2 \log k = \log k^{-2}
\][/tex]
3. Combine the logarithms:
- Use the property that [tex]\(\log a - \log b = \log \left(\frac{a}{b}\right)\)[/tex]:
[tex]\[
\log 9 - \log k^2 = \log \left(\frac{9}{k^2}\right)
\][/tex]
Thus, the expression [tex]\(\log 9 - 2 \log k\)[/tex] can be written as a single logarithm with coefficient 1:
[tex]\[
\log \left(\frac{9}{k^2}\right)
\][/tex]
Therefore, the correct answer is:
[tex]\[
\log \left(\frac{9}{k^2}\right)
\][/tex]
