vereinfachen 0.4log_{2}(1/(0.4))+0.6log_{2}(1/(0.6))

Lösung

vereinfachen

0.4 \cdot lo g_{2} (\frac{1}{0.4}) + 0.6 \cdot lo g_{2} (\frac{1}{0.6})

lo g_{2} (1.96013 \dots)

Dezimale

0.97095 \dots

Schritte zur Lösung

0.4 lo g_{2} (\frac{1}{0.4}) + 0.6 lo g_{2} (\frac{1}{0.6})

Wende die log Regel an:

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

0.4 lo g_{2} (\frac{1}{0.4}) = lo g_{2} ((\frac{1}{0.4})^{0.4})

= lo g_{2} ((\frac{1}{0.4})^{0.4}) + 0.6 lo g_{2} (\frac{1}{0.6})

Wende die log Regel an:

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

0.6 lo g_{2} (\frac{1}{0.6}) = lo g_{2} ((\frac{1}{0.6})^{0.6})

= lo g_{2} ((\frac{1}{0.4})^{0.4}) + lo g_{2} ((\frac{1}{0.6})^{0.6})

Wende die log Regel an:

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

lo g_{2} ((\frac{1}{0.4})^{0.4}) + lo g_{2} ((\frac{1}{0.6})^{0.6}) = lo g_{2} ((\frac{1}{0.4})^{0.4} (\frac{1}{0.6})^{0.6})

= lo g_{2} ((\frac{1}{0.4})^{0.4} (\frac{1}{0.6})^{0.6})

(\frac{1}{0.4})^{0.4} (\frac{1}{0.6})^{0.6} = 1.96013 \dots

= lo g_{2} (1.96013 \dots)

j o in \frac{3 ln ^{2} ( 5 )}{2} - 6 ln^{2} (2)

s im pl i f y 2 lo g_{8} (x) - \frac{1}{2} lo g_{8} (w) + 4 lo g_{8} (y)

s im pl i f y ln (\frac{( 31800000 )}{( 21800 )})

s im pl i f y - lo g_{10} (1.36 \cdot 1 0^{- 5})

s im pl i f y ln (5) + ln (7) - 3 ln^{2} (x)