Questions: Express the following as a sum, difference, or multiple of logarithms. log7(d^5) Choose the correct answer below. A. 5 log7 d B. 5 log d - 7 C. log7 d + 5 D. 7 log d^5

Solution Steps

To express \(\log_{7}(d^5)\) as a sum, difference, or multiple of logarithms, we can use the power rule of logarithms. The power rule states that \(\log_b(a^c) = c \cdot \log_b(a)\). Applying this rule to the given expression, we get:

\[ \log_{7}(d^5) = 5 \cdot \log_{7}(d) \]

So, the correct answer is \(5 \log_{7} d\).

To express \(\log_{7}(d^5)\) in terms of \(\log_{7}(d)\), we use the power rule of logarithms, which states that:

\[ \log_{b}(a^c) = c \cdot \log_{b}(a) \]

In this case, we have \(b = 7\), \(a = d\), and \(c = 5\). Therefore, we can rewrite the expression as:

\[ \log_{7}(d^5) = 5 \cdot \log_{7}(d) \]

From the options provided, we can see that the expression \(5 \cdot \log_{7}(d)\) corresponds to option A.

Final Answer