Question

How do I solve log(x) - log(6) = 2 ?

Answer 1

$\bf \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\stackrel{\textit{we'll use this one}}{\downarrow }}{a^{log_a x}=x} \\\\\\ \textit{Logarithm of rationals} \\\\ log_a\left( \frac{x}{y}\right)\implies log_a(x)-log_a(y) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ log(x)-log(6)=2\implies log\left(\cfrac{x}{6} \right)=2\implies log_{10}\left(\cfrac{x}{6} \right)=2 \\\\\\ 10^{log_{10}\left(\frac{x}{6} \right)}=10^2\implies \cfrac{x}{6}=10^2\implies x=600$