vereinfachen-ln(x)+1/2 ln(b)-ln(c)

Lösung

vereinfachen

- ln (x) + \frac{1}{2} ln (b) - ln (c)

ln (\frac{b ^{\frac{1}{2}}}{c x})

Schritte zur Lösung

- ln (x) + \frac{1}{2} ln (b) - ln (c)

Wende die log Regel an:

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

\frac{1}{2} ln (b) = ln (b^{\frac{1}{2}})

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

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

= ln \frac{\frac{b ^{\frac{1}{2}}}{x}}{c}

Wende Bruchregel an:

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

= ln (\frac{b ^{\frac{1}{2}}}{c x})

e x p an d ln (\frac{e ^{9}}{19})

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