Use the change-of-base property and a calculator to find a decimal approximation to each of the following logarithms (to at least 4 decimal places).
a. $\log _{216} 36=$
b. $\log _{36} 216=$

Step 1 ：Given the logarithms a. $\log _{216} 36=$ and b. $\log _{36} 216=$, we are to find their decimal approximations to at least 4 decimal places.

Step 2 ：We can use the change-of-base property of logarithms, which states that for any positive numbers a, b, and c (where a ≠ 1 and b ≠ 1), the logarithm base b of a number c can be expressed in terms of logarithms with a different base k (where k > 0 and k ≠ 1) as follows: $\log _{b} c = \frac{\log _{k} c}{\log _{k} b}$

Step 3 ：For part a, we can express $\log _{216} 36$ as $\frac{\log _{10} 36}{\log _{10} 216}$ or $\frac{\ln 36}{\ln 216}$.

Step 4 ：Calculating the above expression gives a decimal approximation of 0.6666666666666666 for $\log _{216} 36$.

Step 5 ：Rounding to four decimal places, we get $\log _{216} 36= \boxed{0.6667}$

Step 6 ：For part b, we can express $\log _{36} 216$ as $\frac{\log _{10} 216}{\log _{10} 36}$ or $\frac{\ln 216}{\ln 36}$.

Step 7 ：Calculating the above expression gives a decimal approximation of 1.5000000000000002 for $\log _{36} 216$.

Step 8 ：Rounding to four decimal places, we get $\log _{36} 216= \boxed{1.5000}$