Дано
$$frac{e^{frac{x}{20} left(-1 log{left (3 right )}right)}}{log^{2}{left (3 right )}} left(- 20 x log{left (3 right )} – 400right)$$
Подстановка условия
$$frac{e^{frac{x}{20} left(-1 log{left (3 right )}right)}}{log^{2}{left (3 right )}} left(- 20 x log{left (3 right )} – 400right)$$
((-20*log(3)*(-3/2) – 400)*E^(((-log(3))*(-3/2))/20))/log(3)^2
$$frac{e^{frac{(-3/2)}{20} left(-1 log{left (3 right )}right)}}{log^{2}{left (3 right )}} left(- 20 (-3/2) log{left (3 right )} – 400right)$$
((-20*log(3)*(-3)/2 – 400)*E^(((-log(3))*(-3)/2)/20))/log(3)^2
$$frac{e^{frac{- frac{3}{2}}{20} left(-1 log{left (3 right )}right)}}{log^{2}{left (3 right )}} left(-400 – – 30 log{left (3 right )}right)$$
3^(3/40)*(-400 + 30*log(3))/log(3)^2
$$frac{3^{frac{3}{40}} left(-400 + 30 log{left (3 right )}right)}{log^{2}{left (3 right )}}$$
Степени
$$frac{e^{- frac{x}{20} log{left (3 right )}}}{log^{2}{left (3 right )}} left(- 20 x log{left (3 right )} – 400right)$$
Численный ответ
0.828535449690223*2.71828182845905^(-0.0549306144334055*x)*(-400.0 – 21.9722457733622*x)
Рациональный знаменатель
$$frac{e^{- frac{x}{20} log{left (3 right )}}}{log^{2}{left (3 right )}} left(- 20 x log{left (3 right )} – 400right)$$
Объединение рациональных выражений
$$frac{20 e^{- frac{x}{20} log{left (3 right )}}}{log^{2}{left (3 right )}} left(- x log{left (3 right )} – 20right)$$
Общее упрощение
-x*log(3)
———-
20
-(400 + 20*x*log(3))*e
———————————
2
log (3)
$$- frac{e^{- frac{x}{20} log{left (3 right )}}}{log^{2}{left (3 right )}} left(20 x log{left (3 right )} + 400right)$$
Соберем выражение
$$frac{e^{- frac{x}{20} log{left (3 right )}}}{log^{2}{left (3 right )}} left(- x log{left (3486784401 right )} – 400right)$$
Общий знаменатель
-x*log(3)
———-
20
-(400 + 20*x*log(3))*e
———————————
2
log (3)
$$- frac{e^{- frac{x}{20} log{left (3 right )}}}{log^{2}{left (3 right )}} left(20 x log{left (3 right )} + 400right)$$
Комбинаторика
-x*log(3)
———-
20
-20*(20 + x*log(3))*e
——————————-
2
log (3)
$$- frac{20 e^{- frac{x}{20} log{left (3 right )}}}{log^{2}{left (3 right )}} left(x log{left (3 right )} + 20right)$$
Раскрыть выражение
-x*log(3)
———-
20
(-400 – 20*x*log(3))*e
——————————–
2
log (3)
$$frac{e^{- frac{x}{20} log{left (3 right )}}}{log^{2}{left (3 right )}} left(- 20 x log{left (3 right )} – 400right)$$
