化简 (ln(10))/(2ln(2)-ln(5))

解答

化简

\frac{ln ( 10 )}{2 ln ( 2 ) - ln ( 5 )}

\frac{ln ( 10 )}{ln ( \frac{4}{5} )}

十进制

- 10.31885 \dots

求解步骤

\frac{ln ( 10 )}{2 ln ( 2 ) - ln ( 5 )}

使用对数计算法则:

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

2 ln (2) = ln (2^{2})

= \frac{ln ( 10 )}{ln ( 2 ^{2} ) - ln ( 5 )}

使用对数计算法则:

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

ln (2^{2}) - ln (5) = ln (\frac{2 ^{2}}{5})

= \frac{ln ( 10 )}{ln ( \frac{2 ^{2}}{5} )}

2^{2} = 4

= \frac{ln ( 10 )}{ln ( \frac{4}{5} )}

j o in \frac{9}{10} ln (30)

s im pl i f y ln (\frac{3 x y ^{3}}{3 z})

s im pl i f y - \frac{9}{20} \cdot lo g_{2} (\frac{9}{20}) - \frac{1}{20} \cdot lo g_{2} (\frac{1}{20})

s im pl i f y - \frac{5}{14} \cdot lo g_{2} (\frac{5}{14}) - \frac{9}{14} \cdot lo g_{2} (\frac{9}{14})

e x p an d lo g_{10} ((1 + i)^{- 20})