化简 (ln(15)-ln(2))/(ln(1.05)-ln(1.19))

解答

化简

\frac{ln ( 15 ) - ln ( 2 )}{ln ( 1.05 ) - ln ( 1.19 )}

\frac{ln ( \frac{15}{2} )}{ln ( 0.88235 \dots )}

十进制

- 16.09821 \dots

求解步骤

\frac{ln ( 15 ) - ln ( 2 )}{ln ( 1.05 ) - ln ( 1.19 )}

使用对数计算法则:

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

ln (15) - ln (2) = ln (\frac{15}{2})

= \frac{ln ( \frac{15}{2} )}{ln ( 1.05 ) - ln ( 1.19 )}

使用对数计算法则:

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

ln (1.05) - ln (1.19) = ln (\frac{1.05}{1.19})

= \frac{ln ( \frac{15}{2} )}{ln ( \frac{1.05}{1.19} )}

数字相除:

\frac{1.05}{1.19} = 0.88235 \dots

= \frac{ln ( \frac{15}{2} )}{ln ( 0.88235 \dots )}

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