Question

Solve: 2 In 3 = In(x-4)

Answer 1

`\bf \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( (x)/(y)\right)\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] \rule{34em}{0.25pt}`

`\bf 2\ln(3)=\ln(x-4)\implies \ln(3^2)=\ln(x-4)\implies \ln(9)=\ln(x-4) \\\\\\ \log_e(9)=\log_e(x-4)\implies e^(\log_e(9))=e^(\log_e(x-4))\implies 9=x-4\implies \boxed{13=x}`