de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

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

Lösung

vereinfachen

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

Lösung

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

+1

Dezimale

0.94028 \dots

Schritte zur Lösung

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

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

Schreibe

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

um:

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

Wende die log Regel an:

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

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}} (\frac{5}{14})^{\frac{5}{14}})

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

Vereinfache

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

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

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

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

Multipliziere

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

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

Beliebte Beispiele

erweitern log_{10}((sqrt(xy^7))/(z^3))

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

vereinfachen ln(x)-ln(x+1)

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

erweitern log_{2}((\sqrt[3]{x^4y^7})/z)

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

vereinfachen log_{10}(2/x)

s im pl i f y lo g_{10} (\frac{2}{x})

vereinfachen ln(x)+ln(4)

s im pl i f y ln (x) + ln (4)