Дано
$$frac{log{left (2^{x} – 3 right )}}{6 log{left (2 right )}} – frac{1}{6 log{left (2 right )}} log{left (2^{x} + 3 right )}$$
Подстановка условия
$$frac{log{left (2^{x} – 3 right )}}{6 log{left (2 right )}} – frac{1}{6 log{left (2 right )}} log{left (2^{x} + 3 right )}$$
log(2^(-1/2) – 3)/(6*log(2)) – log(2^(-1/2) + 3)/6*log(2)
$$frac{log{left (2^{(-1/2)} – 3 right )}}{6 log{left (2 right )}} – frac{1}{6 log{left (2 right )}} log{left (2^{(-1/2)} + 3 right )}$$
log(1/sqrt(2) – 3)/(6*log(2)) – log(1/sqrt(2) + 3)/6*log(2)
$$- frac{1}{6 log{left (2 right )}} log{left (frac{1}{sqrt{2}} + 3 right )} + frac{log{left (-3 + frac{1}{sqrt{2}} right )}}{6 log{left (2 right )}}$$
-log(3 + sqrt(2)/2)/(6*log(2)) + (pi*i + log(3 – sqrt(2)/2))/(6*log(2))
$$- frac{log{left (frac{sqrt{2}}{2} + 3 right )}}{6 log{left (2 right )}} + frac{log{left (- frac{sqrt{2}}{2} + 3 right )} + i pi}{6 log{left (2 right )}}$$
Степени
$$frac{log{left (2^{x} – 3 right )}}{6 log{left (2 right )}} – frac{log{left (2^{x} + 3 right )}}{6 log{left (2 right )}}$$
Численный ответ
0.240449173481494*log(2^x – 3) – 0.240449173481494*log(2^x + 3)
Рациональный знаменатель
$$frac{1}{6 log{left (2 right )}} left(log{left (2^{x} – 3 right )} – log{left (2^{x} + 3 right )}right)$$
Объединение рациональных выражений
$$frac{1}{6 log{left (2 right )}} left(log{left (2^{x} – 3 right )} – log{left (2^{x} + 3 right )}right)$$
Общее упрощение
/ x / x
– log3 + 2 / + log -3 + 2 /
—————————-
6*log(2)
$$frac{1}{6 log{left (2 right )}} left(log{left (2^{x} – 3 right )} – log{left (2^{x} + 3 right )}right)$$
Общий знаменатель
/ / x / x
– – log -3 + 2 / + log3 + 2 //
——————————–
6*log(2)
$$- frac{1}{6 log{left (2 right )}} left(- log{left (2^{x} – 3 right )} + log{left (2^{x} + 3 right )}right)$$
Комбинаторика
/ / x / x
– – log -3 + 2 / + log3 + 2 //
——————————–
6*log(2)
$$- frac{1}{6 log{left (2 right )}} left(- log{left (2^{x} – 3 right )} + log{left (2^{x} + 3 right )}right)$$
Раскрыть выражение
/ x / x
log(2)*log3 + 2 / log -3 + 2 /
– —————— + ————
6 6*log(2)
$$frac{log{left (2^{x} – 3 right )}}{6 log{left (2 right )}} – frac{1}{6} log{left (2 right )} log{left (2^{x} + 3 right )}$$
/ x / x
log2 + 3/ log2 – 3/
– ———– + ———–
6*log(2) 6*log(2)
$$frac{log{left (2^{x} – 3 right )}}{6 log{left (2 right )}} – frac{log{left (2^{x} + 3 right )}}{6 log{left (2 right )}}$$
