化简 ln((5ln(L)(2ln(M)))/(1/2 ln(K)))

解答

化简

ln (\frac{5 ln ( L ) ( 2 ln ( M ) )}{\frac{1}{2} ln ( K )})

ln (5) + 2 ln (2) + ln (ln (L)) + ln (ln (M)) - ln (ln (K))

求解步骤

ln (\frac{5 ln ( L ) ( 2 ln ( M ) )}{\frac{1}{2} ln ( K )})

使用对数计算法则:

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

ln (\frac{5 ln ( L ) ( 2 ln ( M ) )}{\frac{1}{2} ln ( K )}) = ln (5 ln (L) (2 ln (M))) - ln (\frac{1}{2} ln (K))

= ln (5 \cdot 2 ln (L) ln (M)) - ln (\frac{1}{2} ln (K))

使用对数计算法则:

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

ln (5 ln (L) \cdot 2 ln (M)) = ln (5) + ln (ln (L)) + ln (2) + ln (ln (M)), ln (\frac{1}{2} ln (K)) = ln (\frac{1}{2}) + ln (ln (K))

= ln (5) + ln (ln (L)) + ln (2) + ln (ln (M)) - (ln (ln (K)) + ln (\frac{1}{2}))

使用对数计算法则:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= ln (5) + ln (ln (L)) + ln (2) + ln (ln (M)) - (ln (ln (K)) - ln (2))

- (- ln (2) + ln (ln (K))) : ln (2) - ln (ln (K))

= ln (5) + ln (ln (L)) + ln (2) + ln (ln (M)) + ln (2) - ln (ln (K))

化简

ln (5) + ln (ln (L)) + ln (2) + ln (ln (M)) + ln (2) - ln (ln (K)) : ln (5) + 2 ln (2) + ln (ln (L)) + ln (ln (M)) - ln (ln (K))

= ln (5) + 2 ln (2) + ln (ln (L)) + ln (ln (M)) - ln (ln (K))

s im pl i f y ln (x) + 3 ln (y) - 5 ln (z)

e x p an d lo g_{2} (\frac{p ^{3} q}{16 r ^{2}})

s im pl i f y \frac{1}{3} ln (\frac{65}{76})

s im pl i f y 3 ln (x) + 4 ln (yz) - ln (x^{2} y^{2})

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