vereinfachen ln((((tan(x))^5))/(e^{2x^4)x^6})

Lösung

vereinfachen

ln \frac{( ( tan ( x ) ) ^{5} )}{e ^{2 x^{4}} x ^{6}}

5 ln (tan (x)) - 2 x^{4} - 6 ln (x)

Schritte zur Lösung

ln \frac{( ( tan ( x ) ) ^{5} )}{e ^{2 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 ^{2 x^{4}} x ^{6}}) = ln ((tan^{5} (x))) - ln (e^{2 x^{4}} x^{6})

= ln (tan^{5} (x)) - ln (e^{2 x^{4}} x^{6})

Wende die log Regel an:

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

ln (tan^{5} (x)) = 5 ln (tan (x))

= 5 ln (tan (x)) - ln (e^{2 x^{4}} x^{6})

Wende die log Regel an:

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

ln (e^{2 x^{4}} x^{6}) = ln (e^{2 x^{4}}) + ln (x^{6})

= 5 ln (tan (x)) - (ln (e^{2 x^{4}}) + ln (x^{6}))

Wende die log Regel an:

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

ln (e^{2 x^{4}}) = 2 x^{4} ln (e)

= 5 ln (tan (x)) - (2 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)

= 5 ln (tan (x)) - (2 x^{4} ln (e) + 6 ln (x))

2 x^{4} ln (e) = 2 x^{4}

= 5 ln (tan (x)) - (2 x^{4} + 6 ln (x))

- (2 x^{4} + 6 ln (x)) : - 2 x^{4} - 6 ln (x)

= 5 ln (tan (x)) - 2 x^{4} - 6 ln (x)

s im pl i f y - lo g_{10} (5.3 \cdot 1 0^{- 13})

e x p an d lo g_{7} ((a b^{6})^{5})

s im pl i f y ln (\frac{4 x ^{2} + 5 x + 4}{x ^{\frac{5}{6}} tan ( x )})

s im pl i f y ln (6) + ln (\frac{e ^{(1.24245)}}{3})

j o in lo g_{10} (7) 37