Fill in the blanks:
a. $\log _{\sqrt{3}}(27)=$
b. $\log _{\sqrt[3]{2}}(8)=$

Step 1 ：The logarithm base b of a number x is the exponent to which b must be raised to get x. In other words, if \(b^y = x\), then \(\log_b(x) = y\). So, to solve these problems, we need to find the exponent that we need to raise the base to in order to get the number inside the logarithm.

Step 2 ：For the first problem, the base is \(\sqrt{3}\) and the number is 27. We need to find the exponent that we need to raise \(\sqrt{3}\) to in order to get 27.

Step 3 ：For the second problem, the base is \(\sqrt[3]{2}\) and the number is 8. We need to find the exponent that we need to raise \(\sqrt[3]{2}\) to in order to get 8.

Step 4 ：The results from the calculations are approximately 6 and 9, respectively. However, due to the precision of calculations, the results are not exact. But we can safely say that \(\log _{\sqrt{3}}(27) \approx 6\) and \(\log _{\sqrt[3]{2}}(8) \approx 9\).

Step 5 ：Final Answer: \(\log _{\sqrt{3}}(27) = \boxed{6}\) and \(\log _{\sqrt[3]{2}}(8) = \boxed{9}\)