Сравните числа (подробно)
1) log(1/2)1/3 и log(1/3)1/2
2) 2^(2log(2)5+log(1/9)9) и √8
Решите уравнение
log(3)x+log(√3)x+log(1/3)x=6
Решить неравенство
log(3√2)(x-5)+log(3√2)(x+12)≤2

$1)/; /; log_{/frac{1}{2}}/frac{1}{3}=log_{2^{-1}}3^{-1}=+log_23////log_23/ /textgreater / log_22=1////log_{/frac{1}{3}}/frac{1}{2}=log_{3^{-1}}2^{-1}=log_32////log_32/ /textless / log_33=1/////Rightarrow /; /; log_23/ /textgreater / log_32/; /; /Rightarrow /underline {log_{/frac{1}{2}}/frac{1}{3}/ /textgreater / log_{/frac{1}{3}}/frac{1}{2}}$

$2)/; /; 2^{2log_25}+log_{/frac{1}{9}}9=2^{log_25^2}+log_{9^{-1}}}9=5^2-log_99=25-1=24/////sqrt8/ /textless / /sqrt9,/; /; /sqrt9=3/; /; /Rightarrow /; /; /; /sqrt8/ /textless / 3////24/ /textgreater / 3/; /; /Rightarrow /; /; (2^{2log_25}+log_{/frac{1}{9}}9)/ /textgreater / /sqrt8$

$3)/; /; log_3x+log_{/sqrt3}x+log_{/frac{1}{3}}x=6/; ,/; /; /; /; ODZ:/; /; x/ /textgreater / 0////log_3x+log_{3^{/frac{1}{2}}}x+log_{3^{-1}}x=6/; /; /; [/, log_{a^{k}}x=/frac{1}{k}log_{a}x/, ]////log_3x-2log_3x-log_3x=6////-2log_3x=6/; /; /to /; /; log_3x=-3/; ,/; /; x=3^{-3}=/frac{1}{27}$

$4)/; /; log_{3/sqrt2}/, (x-5)+log_{3/sqrt2}(x+12) /leq 2/; ,////ODZ:/; ,x/ /textgreater / 5,x/ /textgreater / -12/; /; /; /to /; /; x/ /textgreater / 5////log_{3/sqrt2}( (x-5)/cdot (x+12)) /leq log_{3/sqrt2}(3/sqrt2)^2////(x-5)/cdot (x+12) /leq 18$

$x^2+7x-78 /leq 0////x_1=-13////x_2=6////Otvet:x=6.$