化简 ln((sqrt(1-2cosh(x))(x^3+2))/(x(x-1)))

解答

化简

ln (\frac{1 - 2 cosh ( x ) \cdot ( x ^{3} + 2 )}{x \cdot ( x - 1 )})

ln (1 - 2 cosh (x)) + ln (x^{3} + 2) - ln (x) - ln (x - 1)

求解步骤

ln (\frac{1 - 2 cosh ( x ) ( x ^{3} + 2 )}{x ( x - 1 )})

使用对数计算法则:

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

ln (\frac{1 - 2 cosh ( x ) ( x ^{3} + 2 )}{x ( x - 1 )}) = ln (1 - 2 cosh (x) (x^{3} + 2)) - ln (x (x - 1))

= ln ((x^{3} + 2) - 2 cosh (x) + 1) - ln (x (x - 1))

使用对数计算法则:

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

ln (1 - 2 cosh (x) (x^{3} + 2)) = ln (1 - 2 cosh (x)) + ln (x^{3} + 2), ln (x (x - 1)) = ln (x) + ln (x - 1)

= ln (- 2 cosh (x) + 1) + ln (x^{3} + 2) - (ln (x) + ln (x - 1))

- (ln (x) + ln (x - 1)) : - ln (x) - ln (x - 1)

= ln (1 - 2 cosh (x)) + ln (x^{3} + 2) - ln (x) - ln (x - 1)

s im pl i f y ln (\frac{( ln ( x ) ) ^{x}}{x ^{l n (x)}})

s im pl i f y lo g_{9} (8) - lo g_{9} (7)

s im pl i f y lo g_{4} (10) + lo g_{4} (0.75)

s im pl i f y lo g_{8} (3) + lo g_{8} (5)

s im pl i f y ln (x) + ln (y) - ln (z)