Question

Log 3 + log x = 3 solve for x (show work)

Answer 1

`\begin{array}{llll} \textit{Logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array}~\hfill~ \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{ \textit{we'll use this one} }{a^(log_a (x))=x} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log(3)+\log(x)=3\implies \log(3\cdot x)=3\implies \log(3x)=3 \implies \log_(10)(3x)=3 \\\\\\ 10^{\log_(10)(3x)}=10^3\implies 3x=10^3\implies x=\cfrac{10^3}{3}\implies x=\cfrac{1000}{3}`