vereinfachen ln(m/(2pxpy))-1/2 ln(p)x-1/2 ln(m/(2py))

Lösung

vereinfachen

ln (\frac{m}{2 p x p y}) - \frac{1}{2} ln (p) x - \frac{1}{2} ln (\frac{m}{2 p y})

ln (\frac{2 m y}{2 x y p ^{\frac{3}{2}}}) - \frac{x ln ( p )}{2}

Schritte zur Lösung

ln (\frac{m}{2 p x p y}) - \frac{1}{2} ln (p) x - \frac{1}{2} ln (\frac{m}{2 p y})

Wende die log Regel an:

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

\frac{1}{2} ln (\frac{m}{2 p y}) = ln ((\frac{m}{2 p y})^{\frac{1}{2}})

= ln (\frac{m}{2 pp x y}) - \frac{1}{2} x ln (p) - ln ((\frac{m}{2 p y})^{\frac{1}{2}})

Wende die log Regel an:

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

ln (\frac{m}{2 pp x y}) - ln ((\frac{m}{2 p y})^{\frac{1}{2}}) = ln \frac{\frac{m}{2 pp x y}}{( \frac{m}{2 p y} ) ^{\frac{1}{2}}}

= ln \frac{\frac{m}{2 pp x y}}{( \frac{m}{2 p y} ) ^{\frac{1}{2}}} - \frac{1}{2} x ln (p)

Vereinfache

\frac{\frac{m}{2 p x p y}}{( \frac{m}{2 p y} ) ^{\frac{1}{2}}} : \frac{2 m y}{2 x y p ^{\frac{3}{2}}}

= ln (\frac{2 m y}{2 x y p ^{\frac{3}{2}}}) - \frac{1}{2} ln (p) x

\frac{1}{2} ln (p) x = \frac{x}{2} ln (p)

= ln (\frac{2 m y}{2 x y p ^{\frac{3}{2}}}) - \frac{x}{2} ln (p)

Multipliziere

ln (p) \frac{x}{2} : \frac{x ln ( p )}{2}

= ln (\frac{2 m y}{2 x y p ^{\frac{3}{2}}}) - \frac{x ln ( p )}{2}

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

e x p an d lo g_{4} (\frac{64}{x + 1})

e x p an d lo g_{10} (\frac{x ^{4} 3 z ^{4}}{y})

s im pl i f y 6 ln (x) + 2 ln (y) - 4 ln (z)

s im pl i f y 3 (ln (3) - ln (x^{2})) + (ln (x) - ln (9))