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Реши любую задачу с помощью нейросети.
Дано
$$frac{x}{2} – frac{1}{2 log{left (7 right )}} log{left (7^{x} – 1 right )}$$
Подстановка условия
$$frac{x}{2} – frac{1}{2 log{left (7 right )}} log{left (7^{x} – 1 right )}$$
(-3/2)/2 – log(7^(-3/2) – 1)/2*log(7)
$$frac{(-3/2)}{2} – frac{1}{2 log{left (7 right )}} log{left (7^{(-3/2)} – 1 right )}$$
-3/4 – log(7^(-3/2) – 1)/2*log(7)
$$- frac{3}{4} – frac{1}{2 log{left (7 right )}} log{left (-1 + frac{1}{7 sqrt{7}} right )}$$
-3/4 – (pi*i + log(1 – sqrt(7)/49))/(2*log(7))
$$- frac{3}{4} – frac{log{left (- frac{sqrt{7}}{49} + 1 right )} + i pi}{2 log{left (7 right )}}$$
Степени
$$frac{x}{2} – frac{log{left (7^{x} – 1 right )}}{2 log{left (7 right )}}$$
Численный ответ
0.5*x – 0.256949171184875*log(7^x – 1)
Рациональный знаменатель
$$frac{1}{4 log{left (7 right )}} left(2 x log{left (7 right )} – 2 log{left (7^{x} – 1 right )}right)$$
Объединение рациональных выражений
$$frac{1}{2 log{left (7 right )}} left(x log{left (7 right )} – log{left (7^{x} – 1 right )}right)$$
Общее упрощение
/ x
x log -1 + 7 /
– – ————
2 2*log(7)
$$frac{x}{2} – frac{log{left (7^{x} – 1 right )}}{2 log{left (7 right )}}$$
Соберем выражение
$$frac{x}{2} – frac{1}{2} log{left (7 right )} log{left (7^{x} – 1 right )}$$
Общий знаменатель
/ x
x log -1 + 7 /
– – ————
2 2*log(7)
$$frac{x}{2} – frac{log{left (7^{x} – 1 right )}}{2 log{left (7 right )}}$$
Комбинаторика
/ x
– log -1 + 7 / + x*log(7)
————————-
2*log(7)
$$frac{1}{2 log{left (7 right )}} left(x log{left (7 right )} – log{left (7^{x} – 1 right )}right)$$
Раскрыть выражение
/ x
x log(7)*log -1 + 7 /
– – ——————-
2 2
$$frac{x}{2} – frac{1}{2} log{left (7 right )} log{left (7^{x} – 1 right )}$$
/ x
x log7 – 1/
– – ———–
2 2*log(7)
$$frac{x}{2} – frac{log{left (7^{x} – 1 right )}}{2 log{left (7 right )}}$$