Дано
$$frac{1}{2 cdot 3^{frac{3}{2}}} left(-1 log{left (frac{54 log{left (x right )} – 6 sqrt{3}}{54 log{left (x right )} + 2 cdot 3^{frac{3}{2}}} right )}right)$$
Подстановка условия
$$frac{1}{2 cdot 3^{frac{3}{2}}} left(-1 log{left (frac{54 log{left (x right )} – 6 sqrt{3}}{54 log{left (x right )} + 2 cdot 3^{frac{3}{2}}} right )}right)$$
(-log((54*log((1/2)) – 2*3^(3/2))/(2*3^(3/2) + 54*log((1/2)))))/(2*3^(3/2))
$$frac{1}{2 cdot 3^{frac{3}{2}}} left(-1 log{left (frac{54 log{left ((1/2) right )} – 6 sqrt{3}}{54 log{left ((1/2) right )} + 2 cdot 3^{frac{3}{2}}} right )}right)$$
(-log((54*log(1/2) – 2*3^(3/2))/(2*3^(3/2) + 54*log(1/2))))/(2*3^(3/2))
$$frac{1}{2 cdot 3^{frac{3}{2}}} left(-1 log{left (frac{54 log{left (frac{1}{2} right )} – 6 sqrt{3}}{54 log{left (frac{1}{2} right )} + 2 cdot 3^{frac{3}{2}}} right )}right)$$
-sqrt(3)*log((-54*log(2) – 6*sqrt(3))/(-54*log(2) + 6*sqrt(3)))/18
$$- frac{sqrt{3}}{18} log{left (frac{- 54 log{left (2 right )} – 6 sqrt{3}}{- 54 log{left (2 right )} + 6 sqrt{3}} right )}$$
Степени
$$- frac{sqrt{3}}{18} log{left (frac{54 log{left (x right )} – 6 sqrt{3}}{54 log{left (x right )} + 6 sqrt{3}} right )}$$
Численный ответ
-0.0962250448649376*log((54*log(x) – 2*3^(3/2))/(2*3^(3/2) + 54*log(x)))
Рациональный знаменатель
$$- frac{sqrt{3}}{18} log{left (frac{27 log^{2}{left (x right )} – 6 sqrt{3} log{left (x right )} + 1}{27 log^{2}{left (x right )} – 1} right )}$$
Объединение рациональных выражений
$$- frac{sqrt{3}}{18} log{left (frac{9 log{left (x right )} – sqrt{3}}{9 log{left (x right )} + sqrt{3}} right )}$$
Общее упрощение
/ ___
___ |- / 3 + 9*log(x)|
-/ 3 *log|——————|
| ___ |
/ 3 + 9*log(x) /
——————————-
18
$$- frac{sqrt{3}}{18} log{left (frac{9 log{left (x right )} – sqrt{3}}{9 log{left (x right )} + sqrt{3}} right )}$$
Соберем выражение
$$- frac{sqrt{3}}{18} log{left (frac{log{left (x^{27} right )} – 3 sqrt{3}}{log{left (x^{27} right )} + 3 sqrt{3}} right )}$$
/ 3/2
___ |54*log(x) – 2*3 |
-/ 3 *log|——————|
| 3/2 |
2*3 + 54*log(x)/
——————————-
18
$$- frac{sqrt{3}}{18} log{left (frac{54 log{left (x right )} – 6 sqrt{3}}{54 log{left (x right )} + 2 cdot 3^{frac{3}{2}}} right )}$$
Общий знаменатель
/ ___
___ | / 3 9*log(x) |
-/ 3 *log|- —————- + —————-|
| ___ ___ |
/ 3 + 9*log(x) / 3 + 9*log(x)/
————————————————–
18
$$- frac{sqrt{3}}{18} log{left (frac{9 log{left (x right )}}{9 log{left (x right )} + sqrt{3}} – frac{sqrt{3}}{9 log{left (x right )} + sqrt{3}} right )}$$
Комбинаторика
/ ___
___ | 6*/ 3 54*log(x) |
-/ 3 *log|- ——————- + ——————-|
| ___ ___ |
6*/ 3 + 54*log(x) 6*/ 3 + 54*log(x)/
——————————————————–
18
$$- frac{sqrt{3}}{18} log{left (frac{54 log{left (x right )}}{54 log{left (x right )} + 6 sqrt{3}} – frac{6 sqrt{3}}{54 log{left (x right )} + 6 sqrt{3}} right )}$$
Раскрыть выражение
___ / / ___ / ___
/ 3 * – log – 6*/ 3 + 54*log(x)/ + log6*/ 3 + 54*log(x)//
—————————————————————
18
$$frac{sqrt{3}}{18} left(- log{left (54 log{left (x right )} – 6 sqrt{3} right )} + log{left (54 log{left (x right )} + 6 sqrt{3} right )}right)$$
/ 3/2
___ |54*log(x) – 2*3 |
-/ 3 *log|——————|
| 3/2 |
2*3 + 54*log(x)/
——————————-
18
$$- frac{sqrt{3}}{18} log{left (frac{54 log{left (x right )} – 6 sqrt{3}}{54 log{left (x right )} + 2 cdot 3^{frac{3}{2}}} right )}$$
