簡約 1/2(ln(0.5)-ln(z))/(z/2(ln(2))^2)

解

簡約

\frac{1}{2} \cdot \frac{ln ( 0.5 ) - ln ( z )}{\frac{z}{2} \cdot ( ln ( 2 ) ) ^{2}}

\frac{ln ( \frac{0.5}{z} )}{ln ^{2} ( 2 ) z}

解答ステップ

\frac{1}{2} \cdot \frac{ln ( 0.5 ) - ln ( z )}{\frac{z}{2} ( ln ( 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 (0.5) - ln (z) = ln (\frac{0.5}{z})

= \frac{1}{2} \cdot \frac{ln ( \frac{0.5}{z} )}{\frac{z}{2} ln ^{2} ( 2 )}

\frac{ln ( \frac{0.5}{z} )}{\frac{z}{2} ln ^{2} ( 2 )} = \frac{2 ln ( \frac{0.5}{z} )}{ln ^{2} ( 2 ) z}

= \frac{1}{2} \cdot \frac{2 ln ( \frac{0.5}{z} )}{ln ^{2} ( 2 ) z}

分数を乗じる:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot ln ( \frac{0.5}{z} ) \cdot 2}{2 z ln ^{2} ( 2 )}

共通因数を約分する:

2

= \frac{1 \cdot ln ( \frac{0.5}{z} )}{z ln ^{2} ( 2 )}

乗算:

1 \cdot ln (\frac{0.5}{z}) = ln (\frac{0.5}{z})

= \frac{ln ( \frac{0.5}{z} )}{ln ^{2} ( 2 ) z}