化简 ((-ln| y/x+4|-6ln| y/x-1|))/5+ln(x)

解答

化简

\frac{( - ln \frac{y}{x} + 4 - 6 ln \frac{y}{x} - 1 )}{5} + ln (x)

- \frac{ln ( \frac{y}{x} + 4 ( \frac{y}{x} - 1 ) ^{6} )}{5} + ln (x)

求解步骤

\frac{( - ln \frac{y}{x} + 4 - 6 ln \frac{y}{x} - 1 )}{5} + ln (x)

使用对数计算法则:

a lo g_{c} (b) = lo g_{c} (b^{a})

6 ln \frac{y}{x} - 1 = ln (\frac{y}{x} - 1^{6})

= \frac{( - ln \frac{y}{x} + 4 - ln ( \frac{y}{x} - 1 ^{6} ) )}{5} + ln (x)

将

- ln \frac{y}{x} + 4 - ln (\frac{y}{x} - 1^{6})

改写为

- (ln \frac{y}{x} + 4 + ln (\frac{y}{x} - 1^{6}))

= \frac{( - ( ln \frac{y}{x} + 4 + ln ( \frac{y}{x} - 1 ^{6} ) ) )}{5} + ln (x)

使用对数计算法则:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln \frac{y}{x} + 4 + ln (\frac{y}{x} - 1^{6}) = ln (\frac{y}{x} - 1^{6} \frac{y}{x} + 4)

= \frac{- ln ( \frac{y}{x} - 1 ^{6} \frac{y}{x} + 4 )}{5} + ln (x)

\frac{y}{x} - 1^{6} = (\frac{y}{x} - 1)^{6}

= \frac{- ln ( \frac{y}{x} + 4 ( \frac{y}{x} - 1 ) ^{6} )}{5} + ln (x)

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{ln ( \frac{y}{x} + 4 ( \frac{y}{x} - 1 ) ^{6} )}{5} + ln (x)

s im pl i f y \frac{ln ( a + x ) + ln ( a - x ) - 2 ln ( a )}{x ^{2}}

s im pl i f y ln^{2} (\frac{1}{2}) + 2 ln (\frac{1}{2})

s im pl i f y ln (\frac{729}{4}) - 6 ln (2)

s im pl i f y lo g_{p} (\frac{p - 1}{2 p \cdot ln ( p )})

e x p an d lo g_{10} (2 x^{3})