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( (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((x)/(6) \right)}=10^2\implies \cfrac{x}{6}=10^2\implies x=600`