簡約 1-e^{-θ((yθ)/(-ln(2)-ln(θ)))}

解

簡約

1 - e^{- θ (\frac{y θ}{- l n ( 2 ) - l n ( θ )})}

1 - e^{\frac{θ ^{2} y}{l n ( 2 θ )}}

解答ステップ

1 - e^{- θ (\frac{y θ}{- l n ( 2 ) - l n ( θ )})}

- ln (2) - ln (θ)

を書き換え

- (ln (2) + ln (θ))

= 1 - e^{- (\frac{θ y}{- ( l n ( θ ) + l n ( 2 ) )}) θ}

対数の規則を適用する:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (2) + ln (θ) = ln (2 θ)

= 1 - e^{- θ \frac{y θ}{- l n ( 2 θ )}}

e^{- θ \frac{y θ}{- l n ( 2 θ )}} = e^{\frac{θ ^{2} y}{l n ( 2 θ )}}

= 1 - e^{\frac{θ ^{2} y}{l n ( 2 θ )}}