Дано
$$frac{log{left (frac{3}{4} right )}}{log{left (x right )}} frac{log{left (48 right )}}{log{left (x right )}}$$
Подстановка условия
$$frac{log{left (frac{3}{4} right )}}{log{left (x right )}} frac{log{left (48 right )}}{log{left (x right )}}$$
(log(48)/log((1/3)))*(log(3/4)/log((1/3)))
$$frac{log{left (frac{3}{4} right )}}{log{left ((1/3) right )}} frac{log{left (48 right )}}{log{left ((1/3) right )}}$$
(log(48)/log(1/3))*(log(3/4)/log(1/3))
$$frac{log{left (frac{3}{4} right )}}{log{left (frac{1}{3} right )}} frac{log{left (48 right )}}{log{left (frac{1}{3} right )}}$$
(-log(4) + log(3))*log(48)/log(3)^2
$$frac{log{left (48 right )}}{log^{2}{left (3 right )}} left(- log{left (4 right )} + log{left (3 right )}right)$$
Степени
$$frac{log{left (48 right )}}{log^{2}{left (x right )}} left(- log{left (4 right )} + log{left (3 right )}right)$$
Численный ответ
-1.11367512969541/log(x)^2
Рациональный знаменатель
$$frac{1}{log^{2}{left (x right )}} left(- log{left (4 right )} log{left (48 right )} + log{left (3 right )} log{left (48 right )}right)$$
Объединение рациональных выражений
$$frac{log{left (48 right )}}{log^{2}{left (x right )}} left(- log{left (4 right )} + log{left (3 right )}right)$$
Общее упрощение
/ -log(4) + log(3)
log48 /
———————–
2
log (x)
$$frac{1}{log^{2}{left (x right )}} log{left (48^{- log{left (4 right )} + log{left (3 right )}} right )}$$
Соберем выражение
$$frac{log{left (48 right )}}{log^{2}{left (x right )}} left(- log{left (4 right )} + log{left (3 right )}right)$$
log(48)*log(3/4)
—————-
2
log (x)
$$frac{log{left (frac{3}{4} right )} log{left (48 right )}}{log^{2}{left (x right )}}$$
Общий знаменатель
-(-log(3)*log(48) + 2*log(2)*log(48))
————————————–
2
log (x)
$$- frac{1}{log^{2}{left (x right )}} left(- log{left (3 right )} log{left (48 right )} + 2 log{left (2 right )} log{left (48 right )}right)$$
Комбинаторика
-(-log(3) + 2*log(2))*log(48)
——————————
2
log (x)
$$- frac{log{left (48 right )}}{log^{2}{left (x right )}} left(- log{left (3 right )} + 2 log{left (2 right )}right)$$
Раскрыть выражение
(-log(4) + log(3))*log(48)
————————–
2
log (x)
$$frac{log{left (48 right )}}{log^{2}{left (x right )}} left(- log{left (4 right )} + log{left (3 right )}right)$$
