vereinfachen 1/3 (ln(x+1)-ln(sqrt(x^2-x+1)))

Lösung

vereinfachen

\frac{1}{3} (ln (x + 1) - ln (x^{2} - x + 1))

\frac{ln ( \frac{( x + 1 ) x ^{2} - x + 1}{x ^{2} - x + 1} )}{3}

Schritte zur Lösung

\frac{1}{3} (ln (x + 1) - ln (x^{2} - x + 1))

Wende die log Regel an:

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

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

= \frac{1}{3} ln (\frac{x + 1}{x ^{2} - x + 1})

Vereinfache

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

= \frac{1}{3} ln (\frac{( x + 1 ) x ^{2} - x + 1}{x ^{2} - x + 1})

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot ln ( \frac{( x + 1 ) x ^{2} - x + 1}{x ^{2} - x + 1} )}{3}

Multipliziere:

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

= \frac{ln ( \frac{( x + 1 ) x ^{2} - x + 1}{x ^{2} - x + 1} )}{3}

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

= \frac{ln ( \frac{x + 1}{x ^{2} - x + 1} )}{3}

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

= \frac{ln ( \frac{( x + 1 ) x ^{2} - x + 1}{x ^{2} - x + 1} )}{3}

f a c t or lo g_{10} (\frac{x ^{9}}{y ^{4}})

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

s im pl i f y - 2 - x + ln 1 - \frac{1}{- 2 - x} + x + ln 1 - \frac{1}{x}

s im pl i f y 3 ln (x^{2}) + 5 ln (y) - 2 ln (a) + 4 ln (b^{3}) - 3 ln (c) + 2

s im pl i f y \frac{125 \cdot 1.5 \cdot 1 0 ^{6}}{200 \cdot 25 \cdot 50} \cdot ln (\frac{150}{100})