Question 85475
{{{log(10,3x)+6*(log(10,(x))-log(10,(y)))}}}


{{{log(10,(3x))+6*(log(10,(x/y)))}}} Combine the inner logs by using {{{log(b,x)-log(b,y)=log(b,x/y)}}}


{{{log(10,3x)+log(10,(x/y)^6)}}} Use the identity {{{a*log(b,x)=log(b,x^a)}}} to rewrite {{{6*log(10,x/y)}}} into {{{log(10,(x/y)^6)}}}


{{{log(10,3x)+log(10,(x^6/y^6))}}} Distribute the exponent


{{{log(10,3x*(x^6/y^6))}}} Combine the logs using {{{log(b,x)+log(b,y)=log(b,x*y)}}}


{{{log(10,(3x^7/y^6))}}} Multiply