Using numerical analysis and the Quotient Rule of Logarithms, how can log11(14/t) be rewritten?

1 answer

To rewrite the expression \( \log_{11}(14/t) \) using the Quotient Rule of Logarithms, we start by recalling the Quotient Rule, which states that:

\[ \log_b\left(\frac{A}{B}\right) = \log_b(A) - \log_b(B) \]

In our case, we identify \( A = 14 \) and \( B = t \). Applying the Quotient Rule, we can break down the logarithm as follows:

\[ \log_{11}\left(\frac{14}{t}\right) = \log_{11}(14) - \log_{11}(t) \]

Thus, the expression \( \log_{11}(14/t) \) can be rewritten as:

\[ \log_{11}(14) - \log_{11}(t) \]

This is the simplified form of the logarithmic expression using the Quotient Rule.