Question

Solve In (y-1) - In 2 = x + In x for y

Answer 1

`\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad a^(log_a (x))=x\qquad \leftarrow \textit{we'll be using this one} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \ln(y-1)-\ln(2)=x + \ln(x)\implies \ln(y-1)=x + \ln(x)+\ln(2) \\\\\\ \ln(y-1)=x + \ln(2x)\implies \log_e(y-1)=x + \log_e(2x) \\\\\\ e^(\log_e(y-1))=e^(x + \log_e(2x))\implies y-1=e^(x + \log_e(2x))\implies y=e^(x + \ln(2x)) + 1`