Question

-2 ln (x + 1) - 3 = 7
solve for x

Answer 1

`\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad a^(log_a x)=x\qquad \leftarrow \qquad \textit{let's use this one} \end{array} \\\\[-0.35em] ~\dotfill\\\\ -2\ln(x+1) -3 =7\implies -2\ln(x+1)=10\implies \ln(x+1)=\cfrac{10}{-2} \\\\\\ \ln(x+1)=-5\implies \log_e(x+1)=-5\implies e^(\log_e(x+1))=e^(-5) \\\\\\ x+1=e^(-5)\implies x+1=\cfrac{1}{e^5}\implies x=\cfrac{1}{e^5}-1`