簡約 (3ln(7/4))/(ln(7)-2ln(2))-2

解

簡約

\frac{3 ln ( \frac{7}{4} )}{ln ( 7 ) - 2 ln ( 2 )} - 2

1

解答ステップ

\frac{3 ln ( \frac{7}{4} )}{ln ( 7 ) - 2 ln ( 2 )} - 2

対数の規則を適用する:

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

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

= \frac{3 ln ( \frac{7}{4} )}{ln ( 7 ) - ln ( 2 ^{2} )} - 2

対数の規則を適用する:

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

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

= \frac{3 ln ( \frac{7}{4} )}{ln ( \frac{7}{2 ^{2}} )} - 2

2^{2} = 4

= \frac{3 ln ( \frac{7}{4} )}{ln ( \frac{7}{4} )} - 2

キャンセル

\frac{3 ln ( \frac{7}{4} )}{ln ( \frac{7}{4} )} : 3

= 3 - 2

簡素化

= 1