Дано
$$frac{2 log{left (frac{1}{3} left(a + bright) right )}}{left(frac{log{left (a right )}}{log{left (10 right )}} + frac{log{left (b right )}}{log{left (10 right )}}right) log{left (10 right )}}$$
Подстановка условия
$$frac{2 log{left (frac{1}{3} left(a + bright) right )}}{left(frac{log{left (a right )}}{log{left (10 right )}} + frac{log{left (b right )}}{log{left (10 right )}}right) log{left (10 right )}}$$
(2*log((b + (3))/3))/(log(10)*(log((3))/log(10) + log(b)/log(10)))
$$frac{2 log{left (frac{1}{3} left((3) + bright) right )}}{left(frac{log{left ((3) right )}}{log{left (10 right )}} + frac{log{left (b right )}}{log{left (10 right )}}right) log{left (10 right )}}$$
(2*log((b + 3)/3))/(log(10)*(log(3)/log(10) + log(b)/log(10)))
$$frac{2 log{left (frac{1}{3} left(b + 3right) right )}}{left(frac{log{left (b right )}}{log{left (10 right )}} + frac{log{left (3 right )}}{log{left (10 right )}}right) log{left (10 right )}}$$
2*log(1 + b/3)/((log(3)/log(10) + log(b)/log(10))*log(10))
$$frac{2 log{left (frac{b}{3} + 1 right )}}{left(frac{log{left (b right )}}{log{left (10 right )}} + frac{log{left (3 right )}}{log{left (10 right )}}right) log{left (10 right )}}$$
Степени
$$frac{2 log{left (frac{a}{3} + frac{b}{3} right )}}{left(frac{log{left (a right )}}{log{left (10 right )}} + frac{log{left (b right )}}{log{left (10 right )}}right) log{left (10 right )}}$$
Численный ответ
2.0*log((b + a)/3)/(1.0*log(a) + 1.0*log(b))
Рациональный знаменатель
$$frac{2 log{left (frac{1}{3} left(a + bright) right )}}{log{left (a right )} + log{left (b right )}}$$
Объединение рациональных выражений
$$frac{2 log{left (frac{a}{3} + frac{b}{3} right )}}{log{left (a right )} + log{left (b right )}}$$
Общее упрощение
/a b
2*log|- + -|
3 3/
—————
log(a) + log(b)
$$frac{2 log{left (frac{a}{3} + frac{b}{3} right )}}{log{left (a right )} + log{left (b right )}}$$
Общий знаменатель
-(-2*log(a + b) + 2*log(3))
—————————-
log(a) + log(b)
$$- frac{- 2 log{left (a + b right )} + 2 log{left (3 right )}}{log{left (a right )} + log{left (b right )}}$$
Комбинаторика
/a b
2*log|- + -|
3 3/
—————
log(a) + log(b)
$$frac{2 log{left (frac{a}{3} + frac{b}{3} right )}}{log{left (a right )} + log{left (b right )}}$$
Раскрыть выражение
-2*log(3) + 2*log(a + b)
—————————
/ log(a) log(b)
|——- + ——-|*log(10)
log(10) log(10)/
$$frac{2 log{left (a + b right )} – 2 log{left (3 right )}}{left(frac{log{left (a right )}}{log{left (10 right )}} + frac{log{left (b right )}}{log{left (10 right )}}right) log{left (10 right )}}$$