If $\log _{C} A=1.214$ and $\log _{C} B=1.415$, what is the value of $\log _{c}\left(\frac{B^{2}}{A}\right)$, to the nearest hundredth? Answer:

Step 1 ：Rewrite the expression using properties of logarithms: \(\log _{C}\left(\frac{B^{2}}{A}\right) = \log _{C} B^2 - \log _{C} A\)

Step 2 ：Substitute the given values: \(\log _{C}\left(\frac{B^{2}}{A}\right) = (2 \times 1.415) - 1.214\)

Step 3 ：Calculate the value: \(\log _{C}\left(\frac{B^{2}}{A}\right) = 2.83 - 1.214\)

Step 4 ：Find the final answer: \(\boxed{1.62}\)