Questions: Express as a product. (log C z^-10)

Solution Steps

To express \(\log_{C} z^{-10}\) as a product, we can use the logarithm power rule, which states that \(\log_b (a^n) = n \cdot \log_b (a)\). Applying this rule, we get:

\[ \log_{C} z^{-10} = -10 \cdot \log_{C} z \]

To express \(\log_{C} z^{-10}\) as a product, we use the logarithm power rule, which states that:

\[ \log_b (a^n) = n \cdot \log_b (a) \]

Applying this rule, we have:

\[ \log_{C} z^{-10} = -10 \cdot \log_{C} z \]

For the purpose of this calculation, we substitute \(z = 10\):

\[ \log_{C} z^{-10} = -10 \cdot \log_{C} 10 \]

Using the logarithm base 10, we find:

\[ \log_{C} 10 \approx 1 \]

Thus, the expression simplifies to:

\[ \log_{C} z^{-10} \approx -10 \cdot 1 = -10 \]

Final Answer