合并-(ln(5/22))/(2ln(110/7))

解答

合并

- \frac{ln ( \frac{5}{22} )}{2 ln ( \frac{110}{7} )}

- \frac{ln ( \frac{5}{22} )}{ln ( \frac{12100}{49} )}

十进制

0.26893 \dots

求解步骤

- \frac{ln ( \frac{5}{22} )}{2 ln ( \frac{110}{7} )}

使用对数计算法则:

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

2 ln (\frac{110}{7}) = ln ((\frac{110}{7})^{2})

= - \frac{ln ( \frac{5}{22} )}{ln ( ( \frac{110}{7} ) ^{2} )}

(\frac{110}{7})^{2} = \frac{11 0 ^{2}}{7 ^{2}}

= - \frac{ln ( \frac{5}{22} )}{ln ( \frac{11 0 ^{2}}{7 ^{2}} )}

\frac{11 0 ^{2}}{7 ^{2}} = \frac{12100}{49}

= - \frac{ln ( \frac{5}{22} )}{ln ( \frac{12100}{49} )}

s im pl i f y ln (100 e^{x})

s im pl i f y - ln (\frac{1}{0.99})

s im pl i f y ln (\frac{- 1 \cdot 3 ^{n}}{2 ^{n} b ^{n}})

j o in \frac{1 3 ^{\frac{2 l n ( 2 )}{l n ( 13 )}} + 10}{6}

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