erweitern ln((2^{34/5}x^{15})/(y^{20)})

Lösung

erweitern

ln (\frac{2 ^{\frac{34}{5}} x ^{15}}{y ^{20}})

\frac{34}{5} ln (2) + 15 ln (x) - 20 ln (y)

Schritte zur Lösung

ln (\frac{2 ^{\frac{34}{5}} x ^{15}}{y ^{20}})

Wende die log Regel an:

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

ln (\frac{2 ^{\frac{34}{5}} x ^{15}}{y ^{20}}) = ln (2^{\frac{34}{5}} x^{15}) - ln (y^{20})

= ln (2^{\frac{34}{5}} x^{15}) - ln (y^{20})

Wende die log Regel an:

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

ln (y^{20}) = 20 ln (y)

= ln (2^{\frac{34}{5}} x^{15}) - 20 ln (y)

Wende die log Regel an:

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

ln (2^{\frac{34}{5}} x^{15}) = ln (2^{\frac{34}{5}}) + ln (x^{15})

= ln (2^{\frac{34}{5}}) + ln (x^{15}) - 20 ln (y)

Wende die log Regel an:

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

ln (2^{\frac{34}{5}}) = \frac{34}{5} ln (2)

= \frac{34}{5} ln (2) + ln (x^{15}) - 20 ln (y)

Wende die log Regel an:

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

ln (x^{15}) = 15 ln (x)

= \frac{34}{5} ln (2) + 15 ln (x) - 20 ln (y)

s im pl i f y ln ((t) (t + 4) (t + 6))

s im pl i f y ln (\frac{40}{450})

s im pl i f y \frac{1}{2} ln (2 (9.5) + 1) + 2 ln (9.5 - 1)

e x p an d ln (\frac{7 x y ^{3}}{z})

s im pl i f y 4 lo g_{8} (a) + 16 lo g_{8} (b)