簡約 (3*ln(4))/(8ln(4)-11ln(3))

解

簡約

\frac{3 \cdot ln ( 4 )}{8 ln ( 4 ) - 11 ln ( 3 )}

\frac{6 ln ( 2 )}{ln ( \frac{65536}{177147} )}

十進法表記

- 4.18238 \dots

解答ステップ

\frac{3 ln ( 4 )}{8 ln ( 4 ) - 11 ln ( 3 )}

対数の規則を適用する:

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

8 ln (4) = ln (4^{8})

= \frac{3 ln ( 4 )}{ln ( 4 ^{8} ) - 11 ln ( 3 )}

対数の規則を適用する:

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

11 ln (3) = ln (3^{11})

= \frac{3 ln ( 4 )}{ln ( 4 ^{8} ) - ln ( 3 ^{11} )}

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 (4^{8}) - ln (3^{11}) = ln (\frac{4 ^{8}}{3 ^{11}})

= \frac{3 ln ( 4 )}{ln ( \frac{4 ^{8}}{3 ^{11}} )}

\frac{4 ^{8}}{3 ^{11}} = \frac{65536}{177147}

= \frac{3 ln ( 4 )}{ln ( \frac{65536}{177147} )}

簡素化

ln (4) : 2 ln (2)

= \frac{3 \cdot 2 ln ( 2 )}{ln ( \frac{65536}{177147} )}

数を乗じる:

3 \cdot 2 = 6

= \frac{6 ln ( 2 )}{ln ( \frac{65536}{177147} )}