Use the Laws of Logarithms to expand the expression. \[ \log \left(\sqrt{t^{5}}\right) \]

Step 1 ：Rewrite the square root as a power of 1/2: \(\log \left(t^{5/2}\right)\)

Step 2 ：Use the power rule of logarithms to simplify the expression: \(\frac{5}{2} \cdot \log(t)\)

Step 3 ：The expanded form of the given expression is \(\boxed{\frac{5}{2} \cdot \log(t)}\)