Use the properties of logarithms to rewrite the following expression as a sum or difference of logarithms each of which is the logarithm of an integer or a variable. Assume all variables represent positive real numbers. \[ \log _{10}\left(\frac{7 x}{2}\right) \] \[ \log _{10}\left(\frac{7 x}{2}\right)= \]

Step 1 ：Rewrite the given expression using the property of logarithms \(\log_b(mn) = \log_b(m) + \log_b(n)\): \(\log _{10}\left(\frac{7 x}{2}\right) = \log_{10}(7x) - \log_{10}(2)\)

Step 2 ：Use the property of logarithms again to separate the 7 and x in the first term: \(\log_{10}(7x) = \log_{10}(7) + \log_{10}(x)\)

Step 3 ：Substitute this back into the original expression: \(\log _{10}\left(\frac{7 x}{2}\right) = \log_{10}(7) + \log_{10}(x) - \log_{10}(2)\)

Step 4 ：This is the simplest form of the expression, and it meets the requirements of the problem.