vereinfachen (1/2)^x-1/4 ln(1/x)+arcsin(x)-5/4

Lösung

vereinfachen

(\frac{1}{2})^{x} - \frac{1}{4} ln (\frac{1}{x}) + arcsin (x) - \frac{5}{4}

(\frac{1}{2})^{x} + \frac{1}{4} ln (x) + arcsin (x) - \frac{5}{4}

Schritte zur Lösung

(\frac{1}{2})^{x} - \frac{1}{4} ln (\frac{1}{x}) + arcsin (x) - \frac{5}{4}

Wende die log Regel an:

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

ln (\frac{1}{x}) = ln (1) - ln (x)

= (\frac{1}{2})^{x} - \frac{1}{4} (- ln (x) + ln (1)) + arcsin (x) - \frac{5}{4}

\frac{1}{4} (ln (1) - ln (x)) = - \frac{1}{4} ln (x)

= (\frac{1}{2})^{x} - (- \frac{1}{4} ln (x)) + arcsin (x) - \frac{5}{4}

Wende Regel an

- (- a) = a

= (\frac{1}{2})^{x} + \frac{1}{4} ln (x) + arcsin (x) - \frac{5}{4}

s im pl i f y ln (y) - ln (x) + 1

s im pl i f y - lo g_{10} (2.1 \cdot 1 0^{- 10})

e x p an d lo g_{10} (\frac{4 x ^{2}}{( 3 x y ) ^{5}})

s im pl i f y ln \frac{3 x ^{4} 5 ( x - 1 ) ^{3}}{( 3 x + 1 ) ^{2}}

s im pl i f y \frac{1}{3} ln (x) + \frac{10}{12} ln (x + 3) - \frac{1}{6} ln (x - 3)