Question

Логарифмы! Легко + 40 баллов!
1. $log _{ sqrt{8} } 4 sqrt{2}$
2. $log _{ sqrt{5} } 25 sqrt{5}$
3. $4 ^{2-log_{2} 3}$
4. $25 ^{1+log _{5} 3}$

Answer 1

$=log 2^{3/2}. 2^{5/2}=2/3*5/2log 2, 2=5/3$
$=log 5^{1/2}.5^{5/2}=2*5/2log5.5=5$
$=4^2/4^{log2 .3}=16/2^{2log2.3}=16/3*3=16/9$
$=5^2*5^{2log5.3}=25*3*3=225$