Question 148205
{{{log(2,((4^2)(2^3)))}}} Start with the given expression.



{{{log(2,(((2^2)^2)(2^3)))}}} Rewrite {{{4}}} as {{{2^2}}}



{{{log(2,((2^4)(2^3)))}}} Multiply the exponents.



{{{log(2,(2^7))}}} Multiply the terms by adding the exponents.



{{{7*log(2,(2))}}} Rewrite the expression using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}.




{{{7*1}}} Evaluate {{{log(2,(2))}}} to get 1 



{{{7}}} Multiply



So {{{log(2,((4^2)(2^3)))=7}}}