化简 (ln(5)-2ln(2))/(ln(3)-ln(2))

解答

化简

\frac{ln ( 5 ) - 2 ln ( 2 )}{ln ( 3 ) - ln ( 2 )}

\frac{ln ( \frac{5}{4} )}{ln ( \frac{3}{2} )}

十进制

0.55033 \dots

求解步骤

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

= \frac{ln ( 5 ) - ln ( 2 ^{2} )}{ln ( 3 ) - 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 (5) - ln (2^{2}) = ln (\frac{5}{2 ^{2}})

= \frac{ln ( \frac{5}{2 ^{2}} )}{ln ( 3 ) - ln ( 2 )}

2^{2} = 4

= \frac{ln ( \frac{5}{4} )}{ln ( 3 ) - 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) - ln (2) = ln (\frac{3}{2})

= \frac{ln ( \frac{5}{4} )}{ln ( \frac{3}{2} )}

s im pl i f y 100 ln (\frac{87}{x - 78})

s im pl i f y 6 lo g_{b} (x) + 4 lo g_{b} (z)

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s im pl i f y lo g_{2} (x^{16} 3 y^{17})

s im pl i f y lo g_{5} (\frac{x ^{2}}{y})