Question 202843
{{{log((sqrt(a)/b))}}} Start with the given expression.



{{{log((sqrt(a)))-log((b))}}}  Break up the log using the identity  {{{log((A/B))=log((A))-log((B)))}}}



{{{log((a^(1/2)))-log((b))}}} Convert to exponential notation.



{{{(1/2)log((a))-log((b))}}} Rewrite the first log using the identity  {{{log((x^y))=y*log((x))}}}



{{{(1/2)(0.0441)-0.7964}}} Plug in {{{log((a))=0.0441}}} and {{{log((b))=0.7964}}}



{{{0.02205-0.7964}}} Multiply



{{{-0.77435}}} Combine like terms.



So {{{log((sqrt(a)/b))=-0.77435}}} when {{{log((a))=0.0441}}} and {{{log((b))=0.7964}}}