Question

Найдите значение выражения.$log_{2} log_{2} \sqrt \sqrt[16]{16}$

Answer 1

√¹⁶√16=16^1/32=2^4/32=2^1/8
log 2  2^1/8=1/8=2^(-3)
log2  2^(-3) = -3

Answer 2

$log_{2} log_{2} \sqrt {\sqrt[16]{16}} = log_{2} log_{2} \sqrt[32]{16} = log_{2} log_{2} 16^{1/32} = log_{2} \frac{1}{32} log_{2} 16 = log_{2} \frac{4}{32} = log_{2} \frac{1}{8} = -3.$
Ответ: -3.