化简 (-(y/x)^2)/2+8/7 y/x-3/7 ln(y/x)

解答

化简

\frac{- ( \frac{y}{x} ) ^{2}}{2} + \frac{8}{7} \frac{y}{x} - \frac{3}{7} ln (\frac{y}{x})

- \frac{y ^{2}}{2 x ^{2}} + \frac{8 y}{7 x} - \frac{3}{7} (ln (y) - ln (x))

求解步骤

\frac{- ( \frac{y}{x} ) ^{2}}{2} + \frac{8}{7} \cdot \frac{y}{x} - \frac{3}{7} ln (\frac{y}{x})

使用对数计算法则:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{y}{x}) = ln (y) - ln (x)

= \frac{- ( \frac{y}{x} ) ^{2}}{2} + \frac{8}{7} \cdot \frac{y}{x} - \frac{3}{7} (ln (y) - ln (x))

\frac{- ( \frac{y}{x} ) ^{2}}{2} = - \frac{y ^{2}}{2 x ^{2}}

= - \frac{y ^{2}}{2 x ^{2}} + \frac{8}{7} \cdot \frac{y}{x} - \frac{3}{7} (ln (y) - ln (x))

乘

\frac{8}{7} \cdot \frac{y}{x} : \frac{8 y}{7 x}

= - \frac{y ^{2}}{2 x ^{2}} + \frac{8 y}{7 x} - \frac{3}{7} (ln (y) - ln (x))

s im pl i f y 8.07428 ln \frac{P}{( P - 90 )} - 8.07428 ln (\frac{4}{41})

s im pl i f y e ln (ey) - e - ln (y) + 1

s im pl i f y \frac{1}{\frac{1}{3} - 1} \cdot ln (\frac{0.75 - 1}{0.75 \cdot \frac{1}{3} - 1})

s im pl i f y ln (x - 1) + 2 ln (x + 4) - 3 ln (x - 5)

f a c t or ln (x^{2} + 3) + 2 ln (x) + C