Question

please explain how to solve the attachment.

Answer 1

Using the following rules \(\log(ab)=\log(a)+\log(b)\) and \(\log(\frac{a}{b})=\log(a)-\log(b)\) we get,

\(\log_{10}{\frac{17\sqrt{x}}{y}}=\log_{10}\frac{17x^{\frac{1}{2}}}{y}=\log_{10}(17x^{\frac{1}{2}})-\log_{10}(y)=\log_{10}{17+\log_{10}{x^{\frac{1}{2}}}}-\log_{10}{y}\\ = \log_{10}{17}+\frac{1}{2}\log_{10}{x}-\log_{10}{y}\)