Question

2log4log16 256+ log√2. 8=

Answer 1

$2 log_{ {2}^{2} }( log_{4^{2} }(4^{4} ) ) + log_{ \sqrt{2} }( {2}^{3} ) = \\ = 2 log_{ {2}^{2} }(2) + log_{ 2^{ \frac{1}{2}} }(8) = \\ = 2 log_{ {2}^{2} }(2) + 6 = 2 \times \frac{1}{2} + 6 = \\ = 1 + 6 = 7$
Ответ: 7

Answer 2

Если я правильно понял запись то:
$2 log_{4}( log_{16}(256) ) + log_{ \sqrt{2} }(8) = \\ = log_{ {2}^{2} }( log_{16}( {16}^{2} ) )^{2} + 2 log_{2}( {2}^{3} ) = \\ = log_{ {2}^{2} }(2 ^{2} ) + log_{2}( {2}^{6} ) = \\ = 1 + 6 = 7$