化简-(2ln(2))/(ln(5)-2ln(2))

解答

化简

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

- \frac{2 ln ( 2 )}{ln ( \frac{5}{4} )}

十进制

- 6.21256 \dots

求解步骤

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

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{2 ln ( 2 )}{ln ( 5 ) - ln ( 2 ^{2} )}

使用对数计算法则:

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

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

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

2^{2} = 4

= - \frac{2 ln ( 2 )}{ln ( \frac{5}{4} )}

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

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

s im pl i f y lo g_{a} (\frac{( x - 5 ) ^{6}}{( x + 7 ) ^{7}})

s im pl i f y 5.24 - lo g_{10} (\frac{0.022}{0.1})

s im pl i f y ln (18) - ln (3)