## College Algebra 7th Edition

$92$
Note that $16=2^4$. Thus, the given expression is equivalent to: $=\log_2{[(2^4)^{23}]}$ Using the rule $(a^m)^n=a^{mn}$, the expression above simplifies to: $=\log_2{(2^{4\cdot 23})} \\=\log_2{(2^{92})}$ RECALL: $\log_a{(a^k)} = k$ Use the rule above to obtain: $\log_2{(2^{92})} = 92$