de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

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

Lösung

vereinfachen

- (\frac{5}{14} lo g_{2} (\frac{5}{14}) + \frac{9}{14} lo g_{2} (\frac{9}{14}))

Lösung

- \frac{1}{14} lo g_{2} (\frac{1210689028125}{1 4 ^{14}})

+1

Dezimale

0.94028 \dots

Schritte zur Lösung

- (\frac{5}{14} lo g_{2} (\frac{5}{14}) + \frac{9}{14} lo g_{2} (\frac{9}{14}))

Wende die log Regel an:

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

\frac{5}{14} lo g_{2} (\frac{5}{14}) = lo g_{2} ((\frac{5}{14})^{\frac{5}{14}})

= - (\frac{9}{14} lo g_{2} (\frac{9}{14}) + lo g_{2} ((\frac{5}{14})^{\frac{5}{14}}))

Wende die log Regel an:

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

\frac{9}{14} lo g_{2} (\frac{9}{14}) = lo g_{2} ((\frac{9}{14})^{\frac{9}{14}})

= - (lo g_{2} ((\frac{5}{14})^{\frac{5}{14}}) + lo g_{2} ((\frac{9}{14})^{\frac{9}{14}}))

Wende die log Regel an:

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

lo g_{2} ((\frac{5}{14})^{\frac{5}{14}}) + lo g_{2} ((\frac{9}{14})^{\frac{9}{14}}) = lo g_{2} ((\frac{5}{14})^{\frac{5}{14}} (\frac{9}{14})^{\frac{9}{14}})

= - lo g_{2} ((\frac{5}{14})^{\frac{5}{14}} (\frac{9}{14})^{\frac{9}{14}})

Vereinfache

lo g_{2} ((\frac{5}{14})^{\frac{5}{14}} (\frac{9}{14})^{\frac{9}{14}}) : \frac{1}{14} lo g_{2} ((\frac{9}{14})^{9} (\frac{5}{14})^{5})

= - \frac{1}{14} lo g_{2} ((\frac{9}{14})^{9} (\frac{5}{14})^{5})

(\frac{5}{14})^{5} = \frac{5 ^{5}}{1 4 ^{5}}

= - \frac{1}{14} lo g_{2} ((\frac{9}{14})^{9} \frac{5 ^{5}}{1 4 ^{5}})

(\frac{9}{14})^{9} = \frac{9 ^{9}}{1 4 ^{9}}

= - \frac{1}{14} lo g_{2} (\frac{5 ^{5}}{1 4 ^{5}} \cdot \frac{9 ^{9}}{1 4 ^{9}})

Multipliziere

\frac{5 ^{5}}{1 4 ^{5}} \cdot \frac{9 ^{9}}{1 4 ^{9}} : \frac{1210689028125}{1 4 ^{14}}

= - \frac{1}{14} lo g_{2} (\frac{1210689028125}{1 4 ^{14}})

Beliebte Beispiele

e x p an d x - 2

erweitern (2y^2+3x)dx+(2xy)dy

e x p an d (2 y^{2} + 3 x) d x + (2 x y) d y

erweitern derivative of (3x-3x^2-36)-12

e x p an d \frac{d}{d x} ((3 x - 3 x^{2} - 3) 6) - 12

erweitern (8x^2-6x+3)(8x^2-6x+3)'

e x p an d (8 x^{2} - 6 x + 3) (8 x^{2} - 6 x + 3)^{'}

erweitern (x/(x+1))-(1/x)

e x p an d (\frac{x}{x + 1}) - (\frac{1}{x})