Question

What is the solution of log 2 (3x-7) = 3

Answer 1

$\bf \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_2(3x-7)=3\implies 2^{\log_2(3x-7)}=2^3\implies 3x-7=2^3\implies 3x-7=8 \\\\\\ 3x=15\implies x=\cfrac{15}{3}\implies x=5$