Question 144421
{{{log(2,(3))+log(2,(y^5))-3*log(2,(2x))}}} Start with the given expression



{{{log(2,(3))+log(2,(y^5))-log(2,((2x)^3))}}} Rewrite {{{3*log(2,(2x))}}} as {{{log(2,((2x)^3))}}} using the identity  {{{y*log(b,(x))=log(b,(x^y))}}}



{{{log(2,(3))+log(2,(y^5))-log(2,(8x^3))}}} Cube {{{2x}}} to get {{{8x^3}}}




{{{log(2,(3y^5))-log(2,(8x^3))}}} Combine the first two logs using the identity {{{log(b,(A))+log(b,(B))=log(b,(A*B))}}}



{{{log(2,((3y^5)/(8x^3)))}}} Combine the logs using the identity {{{log(b,(A))-log(b,(B))=log(b,(A/B))}}}



So {{{log(2,(3))+log(2,(y^5))-3*log(2,(2x))}}} simplifies to {{{log(2,((3y^5)/(8x^3)))}}}