vereinfachen 1/5 ln((x^2-25)^5)+ln(e)-ln(1)-ln(x+5)

Lösung

vereinfachen

\frac{1}{5} ln ((x^{2} - 25)^{5}) + ln (e) - ln (1) - ln (x + 5)

ln (x - 5) + 1

Schritte zur Lösung

\frac{1}{5} ln ((x^{2} - 25)^{5}) + ln (e) - ln (1) - ln (x + 5)

Wende die log Regel an:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{5} ln ((x^{2} - 25)^{5}) = ln (((x^{2} - 25)^{5})^{\frac{1}{5}})

= ln (((x^{2} - 25)^{5})^{\frac{1}{5}}) + ln (e) - ln (1) - ln (x + 5)

Wende die log Regel an:

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

ln (((x^{2} - 25)^{5})^{\frac{1}{5}}) - ln (x + 5) = ln \frac{( ( x ^{2} - 25 ) ^{5} ) ^{\frac{1}{5}}}{x + 5}

= ln \frac{( ( x ^{2} - 25 ) ^{5} ) ^{\frac{1}{5}}}{x + 5} + ln (e) - ln (1)

Vereinfache

\frac{( ( x ^{2} - 25 ) ^{5} ) ^{\frac{1}{5}}}{x + 5} : x - 5

= ln (x - 5) + ln (e) - ln (1)

Wende die log Regel an:

lo g_{a} (a) = 1

= ln (x - 5) + 1 - ln (1)

Wende die log Regel an:

lo g_{a} (1) = 0

= ln (x - 5) + 1 - 0

Addiere/Subtrahiere die Zahlen:

1 - 0 = 1

= ln (x - 5) + 1

s im pl i f y ln (\frac{10}{12.5}) + ln (\frac{8}{10})

e x p an d ln (\frac{x}{x - 2})

e x p an d lo g_{2} (\frac{16}{x ^{4}})

s im pl i f y 5 lo g_{3} (z) + 7 lo g_{3} (y)

s im pl i f y 1.76776 ln (\frac{1}{( 2 2 )})