Use the Laws of Logarithms to expand the expression.
\[
\log \left(\sqrt{t^{5}}\right)
\]
The expanded form of the given expression is \(\boxed{\frac{5}{2} \cdot \log(t)}\)
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 \(\boxed{\frac{5}{2} \cdot \log(t)}\)