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

Answer 1

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.