Question

Чему равно выражение. Даю 50)

Answer 1

$displaystyle frac{log_312}{log_{36}9}- frac{log_32}{log_{108}3}= frac{log_312}{ frac{1}{log_{3^2}36}}- frac{log_32}{ frac{1}{log_3108}}=\=log_312*log_{3^2}36-log_32*log_3108=\= frac{1}{2}log_312*log_336-log_32(log_33+log_336)=\= frac{1}{2}log_312*log_336-log_32-log_32*log_336=\=log_336( frac{1}{2}log_312-log_32)-log_32=\=log_336( frac{1}{2}(log_33+log_32^2)-log_32)-log_32=\=log_336( frac{1}{2}+log_32-log_32)-log_32=\= frac{1}{2}(log_33^2+log_32^2)-log_32=1+log_32-log_32=1$