Question 149752
{{{log(10,(r))-log(10,(t))+2log(10,(s))}}} Start with the given expression.



{{{log(10,(r))-log(10,(t))+log(10,(s^2))}}} Rewrite {{{2log(10,(s))}}} as {{{log(10,(s^2))}}} using the identity  {{{y*log(b,(x))=log(b,(x^y))}}}



{{{log(10,(r/t))+log(10,(s^2))}}} Combine the logs using the identity {{{log(b,(A))-log(b,(B))=log(b,(A/B))}}}



{{{log(10,((r/t)(s^2)))}}} Combine the logs using the identity {{{log(b,(A))+log(b,(B))=log(b,(A*B))}}}



{{{log(10,(rs^2/t)))}}} Simplify.



So {{{log(10,(r))-log(10,(t))+2log(10,(s))}}} simplifies to {{{log(10,(rs^2/t)))}}}