Question

Which expression is equivalent to
logbase12 ((1/2)/8w)?

Answer 1

`\bf \begin{array}{llll} \textit{logarithm of factors} \\\\ log_a(xy)\implies log_a(x)+log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm of rationals} \\\\ log_a\left( (x)/(y)\right)\implies log_a(x)-log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}`

`\bf \log_(12)\left( \cfrac{~~(1)/(2)~~}{8w} \right)\implies \begin{array}{llll} \log_(12)\left( (1)/(2) \right)&-&\log_(12)(8w)\\\\ \log_(12)(1)-\log_(12)(2)&-&[\log_(12)(8)+\log_(12)(w)] \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \log_(12)(1)-\log_(12)(2)-\log_(12)(8)-\log_(12)(w)~\hfill`