Question 196669
{{{log(2,(48))-(1/3)log(2,(27))}}} Start with the given expression.



{{{log(2,(48))-log(2,(27^(1/3)))}}} Rewrite the second log using the identity  {{{y*log(b,(x))=log(b,(x^y))}}}



{{{log(2,(48))-log(2,(root(3,27)))}}} Convert to radical form.



{{{log(2,(48))-log(2,(3))}}} Evaluate the cube root of 27 to get 3



{{{log(2,(48/3))}}} Combine the logs using the identity {{{log(b,(A))-log(b,(B))=log(b,(A/B))}}}



{{{log(2,(16))}}} Reduce



{{{log(2,(2^4))}}} Rewrite {{{16}}} as {{{2^4}}}



{{{4*log(2,(2))}}} Pull down the exponent using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}



{{{4*1}}} Evaluate the log base 2 of 2 to get 1



{{{4}}} Multiply



So {{{log(2,(48))-(1/3)log(2,(27))=4}}}