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?
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Answer

Find the final answer: $\boxed{1.62}$

Steps

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: $\boxed{1.62}$