de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

vereinfachen-9/20log_{2}(9/20)-1/20log_{2}(1/20)

Lösung

vereinfachen

- \frac{9}{20} \cdot lo g_{2} (\frac{9}{20}) - \frac{1}{20} \cdot lo g_{2} (\frac{1}{20})

Lösung

- \frac{1}{20} lo g_{2} (\frac{387420489}{2 0 ^{10}})

+1

Dezimale

0.73449 \dots

Schritte zur Lösung

- \frac{9}{20} lo g_{2} (\frac{9}{20}) - \frac{1}{20} lo g_{2} (\frac{1}{20})

Wende die log Regel an:

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

\frac{9}{20} lo g_{2} (\frac{9}{20}) = lo g_{2} ((\frac{9}{20})^{\frac{9}{20}})

= - lo g_{2} ((\frac{9}{20})^{\frac{9}{20}}) - \frac{1}{20} lo g_{2} (\frac{1}{20})

Wende die log Regel an:

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

\frac{1}{20} lo g_{2} (\frac{1}{20}) = lo g_{2} ((\frac{1}{20})^{\frac{1}{20}})

= - lo g_{2} ((\frac{9}{20})^{\frac{9}{20}}) - lo g_{2} ((\frac{1}{20})^{\frac{1}{20}})

Schreibe

- lo g_{2} ((\frac{9}{20})^{\frac{9}{20}}) - lo g_{2} ((\frac{1}{20})^{\frac{1}{20}})

um:

- (lo g_{2} ((\frac{9}{20})^{\frac{9}{20}}) + lo g_{2} ((\frac{1}{20})^{\frac{1}{20}}))

= - (lo g_{2} ((\frac{9}{20})^{\frac{9}{20}}) + lo g_{2} ((\frac{1}{20})^{\frac{1}{20}}))

Wende die log Regel an:

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

lo g_{2} ((\frac{9}{20})^{\frac{9}{20}}) + lo g_{2} ((\frac{1}{20})^{\frac{1}{20}}) = lo g_{2} ((\frac{9}{20})^{\frac{9}{20}} (\frac{1}{20})^{\frac{1}{20}})

= - lo g_{2} ((\frac{9}{20})^{\frac{9}{20}} (\frac{1}{20})^{\frac{1}{20}})

Vereinfache

lo g_{2} ((\frac{9}{20})^{\frac{9}{20}} (\frac{1}{20})^{\frac{1}{20}}) : \frac{1}{20} lo g_{2} ((\frac{9}{20})^{9} \frac{1}{20})

= - \frac{1}{20} lo g_{2} ((\frac{9}{20})^{9} \frac{1}{20})

(\frac{9}{20})^{9} = \frac{9 ^{9}}{2 0 ^{9}}

= - \frac{1}{20} lo g_{2} (\frac{1}{20} \cdot \frac{9 ^{9}}{2 0 ^{9}})

Multipliziere

\frac{9 ^{9}}{2 0 ^{9}} \cdot \frac{1}{20} : \frac{387420489}{2 0 ^{10}}

= - \frac{1}{20} lo g_{2} (\frac{387420489}{2 0 ^{10}})

Beliebte Beispiele

vereinfachen-5/14*log_{2}(5/14)-9/14*log_{2}(9/14)

s im pl i f y - \frac{5}{14} \cdot lo g_{2} (\frac{5}{14}) - \frac{9}{14} \cdot lo g_{2} (\frac{9}{14})

erweitern log_{10}((1+i)^{-20})

e x p an d lo g_{10} ((1 + i)^{- 20})

vereinfachen ln(55/50)+((0.06+0.4)*0.5)

s im pl i f y ln (\frac{55}{50}) + ((0.06 + 0.4) \cdot 0.5)

erweitern log_{10}((7y^3)/(4x^2))

e x p an d lo g_{10} (\frac{7 y ^{3}}{4 x ^{2}})

vereinfachen (-0.94+1.96*0.21)*(ln(7.9)-ln(7.5)*100)

s im pl i f y (- 0.94 + 1.96 \cdot 0.21) \cdot (ln (7.9) - ln (7.5) \cdot 100)