簡約 ln(e^{ln(x)}(e^{ln(ex)}))

解

簡約

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

2 ln (x) + 1

解答ステップ

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

対数の規則を適用する:

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

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

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

対数の規則を適用する:

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

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

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

対数の規則を適用する:

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

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

= ln (x) ln (e) + ln (e x) ln (e)

対数の規則を適用する:

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

ln (e x) ln (e) = ln (e) ln (e) + ln (e) ln (x)

= ln (e) ln (x) + ln (e) ln (e) + ln (e) ln (x)

簡素化

ln (x) ln (e) + ln (e) ln (e) + ln (e) ln (x) : 2 ln (e) ln (x) + ln (e) ln (e)

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

ln (e) ln (e) = 1

= 2 ln (x) + 1