erweitern ln(ln((sinh(x)+cosh(x))^2))

Lösung

erweitern

ln (ln ((sinh (x) + cosh (x))^{2}))

ln (2) + ln (ln (sinh (x) + cosh (x)))

Schritte zur Lösung

ln (ln ((sinh (x) + cosh (x))^{2}))

Wende die log Regel an:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((sinh (x) + cosh (x))^{2}) = 2 ln (sinh (x) + cosh (x))

= ln (2 ln (sinh (x) + cosh (x)))

Wende die log Regel an:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (2 ln (sinh (x) + cosh (x))) = ln (2) + ln (ln (sinh (x) + cosh (x)))

= ln (2 ln (sinh (x) + cosh (x)))

Wende die log Regel an:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (2 ln (sinh (x) + cosh (x))) = ln (2) + ln (ln (sinh (x) + cosh (x)))

= ln (2) + ln (ln (sinh (x) + cosh (x)))

s im pl i f y 2 lo g_{6} (x) - 3 lo g_{6} (y)

s im pl i f y lo g_{10} (\frac{7 x ( 2 - x )}{2 ( x - 1 ) ^{3}})

s im pl i f y ln (\frac{1000000}{415382})

s im pl i f y lo g_{10} (x) - 6 lo g_{10} (y) + 7 lo g_{10} (z)

e x p an d ln (\frac{e ^{5}}{11})