Question

Логарифм....
......
.....

​

Answer 1

$0.25(1 + 4 {}^{ log_{2}5} ) log_{26}4 = 0.25 log_{26}4 + log_{26}4 log_{2}5 = 0.25 log_{26}2 ^{2} + log_{26}2 ^{2} log_{2}5 = 0.25 \times 2 log_{26}2 + 2 log_{26}2 log_{2}5 = 0.5 log_{26}2 + 2 log_{26} 2 \times \frac{ log_{26}5}{ log_{26}2 } = log_{26}2 ^{0.5} + 2 log_{26}5 = log_{26}2 ^{0.5} + log_{26}5 ^{2} = log_{26}2 ^{0.5} \times 5 ^{2} = log_{26}25 \times 2 ^{ \frac{1}{2} } = log_{26}25 \sqrt{2}$