vereinfachen-[-3/10 ln(3)+8/35 ln(8)+15/14 ln(1)]

Lösung

vereinfachen

- [- \frac{3}{10} ln (3) + \frac{8}{35} ln (8) + \frac{15}{14} ln (1)]

- ln (\frac{8 ^{\frac{8}{35}} \cdot 3 ^{\frac{7}{10}}}{3})

Dezimale

- 0.14571 \dots

Schritte zur Lösung

- [- \frac{3}{10} ln (3) + \frac{8}{35} ln (8) + \frac{15}{14} ln (1)]

Wende die log Regel an:

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

\frac{3}{10} ln (3) = ln (3^{\frac{3}{10}})

= - [\frac{8}{35} ln (8) + \frac{15}{14} ln (1) - ln (3^{\frac{3}{10}})]

Wende die log Regel an:

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

\frac{8}{35} ln (8) = ln (8^{\frac{8}{35}})

= - [\frac{15}{14} ln (1) + ln (8^{\frac{8}{35}}) - ln (3^{\frac{3}{10}})]

Wende die log Regel an:

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

ln (8^{\frac{8}{35}}) - ln (3^{\frac{3}{10}}) = ln (\frac{8 ^{\frac{8}{35}}}{3 ^{\frac{3}{10}}})

= - [\frac{15}{14} ln (1) + ln (\frac{8 ^{\frac{8}{35}}}{3 ^{\frac{3}{10}}})]

\frac{8 ^{\frac{8}{35}}}{3 ^{\frac{3}{10}}} = \frac{8 ^{\frac{8}{35}} \cdot 3 ^{\frac{7}{10}}}{3}

= - [ln (\frac{8 ^{\frac{8}{35}} \cdot 3 ^{\frac{7}{10}}}{3}) + \frac{15}{14} ln (1)]

\frac{15}{14} ln (1) = 0

= - (ln (\frac{8 ^{\frac{8}{35}} \cdot 3 ^{\frac{7}{10}}}{3}) + 0)

ln (\frac{8 ^{\frac{8}{35}} \cdot 3 ^{\frac{7}{10}}}{3}) + 0 = ln (\frac{8 ^{\frac{8}{35}} \cdot 3 ^{\frac{7}{10}}}{3})

= - ln (\frac{8 ^{\frac{8}{35}} \cdot 3 ^{\frac{7}{10}}}{3})

s im pl i f y lo g_{10} (x^{2} - 7 x - 8) - lo g_{10} (x^{2} - 1)

s im pl i f y ln (\frac{( c ^{1 - n} m ^{n} ) ^{1 - l}}{1 - l})

s im pl i f y 20 lo g_{10} (2) + 40 lo g_{10} (0.04)

s im pl i f y lo g_{9} (\frac{4 7}{s ^{2} r})

s im pl i f y lo g_{3} (\frac{1}{16}) - 1