vereinfachen 1/9 ln(x-15)-1/9 ln(x-6)

Lösung

vereinfachen

\frac{1}{9} ln (x - 15) - \frac{1}{9} ln (x - 6)

ln (9 \frac{x - 15}{x - 6})

Schritte zur Lösung

\frac{1}{9} ln (x - 15) - \frac{1}{9} ln (x - 6)

Wende die log Regel an:

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

\frac{1}{9} ln (x - 15) = ln ((x - 15)^{\frac{1}{9}})

= ln ((x - 15)^{\frac{1}{9}}) - \frac{1}{9} ln (x - 6)

Wende die log Regel an:

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

\frac{1}{9} ln (x - 6) = ln ((x - 6)^{\frac{1}{9}})

= ln ((x - 15)^{\frac{1}{9}}) - ln ((x - 6)^{\frac{1}{9}})

Wende die log Regel an:

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

ln ((x - 15)^{\frac{1}{9}}) - ln ((x - 6)^{\frac{1}{9}}) = ln (\frac{( x - 15 ) ^{\frac{1}{9}}}{( x - 6 ) ^{\frac{1}{9}}})

= ln (\frac{( x - 15 ) ^{\frac{1}{9}}}{( x - 6 ) ^{\frac{1}{9}}})

Fasse gleiche Potenzen zusammen:

\frac{x ^{\frac{a}{m}}}{y ^{\frac{b}{m}}} = m \frac{x ^{a}}{y ^{b}}

= ln (9 \frac{x - 15}{x - 6})

so l v e f or t, s t + 1 = t^{2} + s

z^{2} = 4 + 4 r^{2}

(1 - 2 x) (1 - 3 x) = (5 x - 1) x - 2 (2 x - 5)

2 x^{2} + 16 x - 96 = 0

co m pl e t es q u a re 3 x^{2} + 12 x - 4