Question

What is the value of x if e^3x+6 = 8?

Answer 1

`\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^(log_a (x))=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ e^(3x+6)=8\implies \log_e(e^(3x+6))=\log_e(8)\implies 3x+6=\log_e(8) \\\\\\ 3x+6=\ln(8)\implies 3x=\ln(8)-6\implies x=\cfrac{\ln(8)-6}{3}`