vereinfachen (2ln((x-10)^3))/3-ln(x(x-10))

Lösung

vereinfachen

\frac{2 ln ( ( x - 10 ) ^{3} )}{3} - ln (x (x - 10))

ln (x - 10) - ln (x)

Schritte zur Lösung

\frac{2 ln ( ( x - 10 ) ^{3} )}{3} - ln (x (x - 10))

Wende die log Regel an:

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

ln (x (x - 10)) = ln (x) + ln (x - 10)

= \frac{2 ln ( ( x - 10 ) ^{3} )}{3} - (ln (x) + ln (x - 10))

Wende die log Regel an:

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

ln ((x - 10)^{3}) = 3 ln (x - 10)

= \frac{2 \cdot 3 ln ( x - 10 )}{3} - (ln (x) + ln (x - 10))

\frac{2 \cdot 3 ln ( x - 10 )}{3} = 2 ln (x - 10)

= 2 ln (x - 10) - (ln (x) + ln (x - 10))

- (ln (x) + ln (x - 10)) : - ln (x) - ln (x - 10)

= 2 ln (x - 10) - ln (x) - ln (x - 10)

Addiere gleiche Elemente:

2 ln (x - 10) - ln (x - 10) = ln (x - 10)

= ln (x - 10) - ln (x)

e x p an d lo g_{10} (\frac{5 x}{4 y})

s im pl i f y ln (\frac{x ^{\frac{1}{2}} ( 2 x + 7 ) ^{4}}{( 3 x ^{2} + 1 ) ^{2}})

s im pl i f y lo g_{2} (3) + 4 lo g_{2} (x) - 6 lo g_{2} (y)

s im pl i f y 7 lo g_{3} (k) + 6 lo g_{3} (m) - 9 lo g_{3} (n)

s im pl i f y ln (4) + 2 ln (3)