Question

Вычислите:

log2(10)*log3(2)* log4(3)* log5(4)*...*log1000(999)

Answer 1

$log_{2}10*log_{3}2*log_{4}3*log_{5}4*...*log_{1000}999$

перейдем к основанию 2:

$log_{2}10*frac{log_{2}2}{log_{2}3}*frac{log_{2}3}{log_{2}4}*frac{log_{2}4}{log_{2}5}*...*frac{log_{2}999}{log_{2}1000}=\ =frac{log_{2}10}{log_{2}1000}=\ = frac{log_{2}10}{log_{2}10^{3}}=\ =frac{log_{2}10}{3log_{2}10}=frac{1}{3}$