化简 (8ln(3))/(2ln(3)-ln(2))

解答

化简

\frac{8 ln ( 3 )}{2 ln ( 3 ) - ln ( 2 )}

\frac{8 ln ( 3 )}{ln ( \frac{9}{2} )}

十进制

5.84338 \dots

求解步骤

\frac{8 ln ( 3 )}{2 ln ( 3 ) - ln ( 2 )}

使用对数计算法则:

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

2 ln (3) = ln (3^{2})

= \frac{8 ln ( 3 )}{ln ( 3 ^{2} ) - ln ( 2 )}

使用对数计算法则:

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

ln (3^{2}) - ln (2) = ln (\frac{3 ^{2}}{2})

= \frac{8 ln ( 3 )}{ln ( \frac{3 ^{2}}{2} )}

3^{2} = 9

= \frac{8 ln ( 3 )}{ln ( \frac{9}{2} )}

e x p an d lo g_{10} (4 x^{5})

s im pl i f y ln (0.019 \cdot 1.78108)

e x p an d lo g_{6} (\frac{5}{12 x})

s im pl i f y ln (3 3 x)

s im pl i f y ln (\frac{41}{13})