Expand the logarithm expression \(\log_{2}(16x^3)\)

Step 1 ：Applying the properties of logarithms, we can break the logarithm apart into the sum of two separate logs: \(\log_{2}(16x^3) = \log_{2}(16) + \log_{2}(x^3)\)

Step 2 ：Now simplify \(\log_{2}(16)\) to 4 because 2 raised to the power of 4 equals 16: \(\log_{2}(16x^3) = 4 + \log_{2}(x^3)\)

Step 3 ：Next, apply the power rule of logarithms to bring down the exponent in \(\log_{2}(x^3)\): \(\log_{2}(16x^3) = 4 + 3\log_{2}(x)\)