簡約 ln((e^{xln(2)})/2)

解

簡約

ln (\frac{e ^{x l n (2)}}{2})

ln (2) x - ln (2)

解答ステップ

ln (\frac{e ^{x l n (2)}}{2})

対数の規則を適用する:

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

ln (\frac{e ^{x l n (2)}}{2}) = ln (e^{x l n (2)}) - ln (2)

= ln (e^{l n (2) x}) - ln (2)

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{x l n (2)}) = x ln (2) ln (e)

= x ln (2) ln (e) - ln (2)

x ln (2) ln (e) = ln (2) x

= ln (2) x - ln (2)