vereinfachen ln((e^9)/(xy^8))

Lösung

vereinfachen

ln (\frac{e ^{9}}{x y ^{8}})

9 - ln (x) - 8 ln (y)

Schritte zur Lösung

ln (\frac{e ^{9}}{x y ^{8}})

Wende die log Regel an:

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

ln (\frac{e ^{9}}{x y ^{8}}) = ln (e^{9}) - ln (x y^{8})

= ln (e^{9}) - ln (x y^{8})

Wende die log Regel an:

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

ln (e^{9}) = 9 ln (e)

= 9 ln (e) - ln (x y^{8})

Wende die log Regel an:

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

ln (x y^{8}) = ln (x) + ln (y^{8})

= 9 ln (e) - (ln (x) + ln (y^{8}))

Wende die log Regel an:

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

ln (y^{8}) = 8 ln (y)

= 9 ln (e) - (ln (x) + 8 ln (y))

9 ln (e) = 9

= 9 - (ln (x) + 8 ln (y))

- (ln (x) + 8 ln (y)) : - ln (x) - 8 ln (y)

= 9 - ln (x) - 8 ln (y)

s im pl i f y ln (\frac{3}{3} - 1) - ln (\frac{3}{3} + 1)

s im pl i f y \frac{4 π \cdot 1 0 ^{- 7} \cdot 10 ( 0.2 )}{2 π} [ln (0.18) - ln (0.08)]

e x p an d lo g_{2} (32 (x + 5)^{4})

s im pl i f y \frac{1}{( 1 + 2 - 1 )} \cdot ln (\frac{1}{1 - 2})

s im pl i f y \frac{1}{- 0.10986} ln (\frac{40}{60})