vereinfachen ln((tan^5(x))/(e^{6x^4)x^6})

Lösung

vereinfachen

ln (\frac{tan ^{5} ( x )}{e ^{6 x^{4}} x ^{6}})

ln (tan^{5} (x)) - 6 x^{4} - 6 ln (x)

Schritte zur Lösung

ln (\frac{tan ^{5} ( x )}{e ^{6 x^{4}} x ^{6}})

Wende die log Regel an:

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

ln (\frac{tan ^{5} ( x )}{e ^{6 x^{4}} x ^{6}}) = ln (tan^{5} (x)) - ln (e^{6 x^{4}} x^{6})

= ln (tan^{5} (x)) - ln (e^{6 x^{4}} x^{6})

Wende die log Regel an:

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

ln (e^{6 x^{4}} x^{6}) = ln (e^{6 x^{4}}) + ln (x^{6})

= ln (tan^{5} (x)) - (ln (e^{6 x^{4}}) + ln (x^{6}))

Wende die log Regel an:

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

ln (e^{6 x^{4}}) = 6 x^{4} ln (e)

= ln (tan^{5} (x)) - (6 x^{4} ln (e) + ln (x^{6}))

Wende die log Regel an:

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

ln (x^{6}) = 6 ln (x)

= ln (tan^{5} (x)) - (6 x^{4} ln (e) + 6 ln (x))

6 x^{4} ln (e) = 6 x^{4}

= ln (tan^{5} (x)) - (6 x^{4} + 6 ln (x))

- (6 x^{4} + 6 ln (x)) : - 6 x^{4} - 6 ln (x)

= ln (tan^{5} (x)) - 6 x^{4} - 6 ln (x)

s im pl i f y 2 lo g_{10} (x) - lo g_{10} (x + 2)

s im pl i f y - ln 900 - x^{2} + 2 ln (30)

s im pl i f y ln (\frac{121}{13})

s im pl i f y 8.64 + lo g_{10} (\frac{0.89}{0.25})

s im pl i f y ln (\frac{1 - e ^{- u}}{u})