Express in terms of sums and differences of logarithms. \[ \log \sqrt{c^{3} d} \] \[ \log \sqrt{c^{3} d}= \] (Use integers or fractions for any numbers in the expression.)

Step 1 ：The given expression is a logarithm of a square root of a product. We can simplify this using the properties of logarithms. The square root of a number is the same as raising that number to the 1/2 power. The logarithm of a product is the sum of the logarithms of the factors. The logarithm of a number raised to a power is the product of the power and the logarithm of the number.

Step 2 ：First, we can rewrite the square root as a power of 1/2: \(\log ((c^{3}d)^{1/2})\).

Step 3 ：Next, we can use the property of logarithms that the logarithm of a number raised to a power is the product of the power and the logarithm of the number. This gives us: \(0.5 \log (c^{3}d)\).

Step 4 ：Finally, we can use the property of logarithms that the logarithm of a product is the sum of the logarithms of the factors. This gives us: \(0.5 \log c^{3} + 0.5 \log d\).

Step 5 ：Applying the property of logarithms that the logarithm of a number raised to a power is the product of the power and the logarithm of the number, we get: \(1.5 \log c + 0.5 \log d\).

Step 6 ：So, the expression \(\log \sqrt{c^{3} d}\) can be expressed in terms of sums and differences of logarithms as \(\boxed{1.5 \log c + 0.5 \log d}\).