vereinfachen-0.6log_{2}(0.6)-0.4log_{2}(0.4)

Lösung

vereinfachen

- 0.6 \cdot lo g_{2} (0.6) - 0.4 \cdot lo g_{2} (0.4)

- lo g_{2} (0.51016 \dots)

Dezimale

0.97095 \dots

Schritte zur Lösung

- 0.6 lo g_{2} (0.6) - 0.4 lo g_{2} (0.4)

Wende die log Regel an:

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

0.6 lo g_{2} (0.6) = lo g_{2} (0. 6^{0.6})

= - lo g_{2} (0. 6^{0.6}) - 0.4 lo g_{2} (0.4)

Wende die log Regel an:

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

0.4 lo g_{2} (0.4) = lo g_{2} (0. 4^{0.4})

= - lo g_{2} (0. 6^{0.6}) - lo g_{2} (0. 4^{0.4})

Schreibe

- lo g_{2} (0. 6^{0.6}) - lo g_{2} (0. 4^{0.4})

um:

- (lo g_{2} (0. 6^{0.6}) + lo g_{2} (0. 4^{0.4}))

= - (lo g_{2} (0. 6^{0.6}) + lo g_{2} (0. 4^{0.4}))

Wende die log Regel an:

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

lo g_{2} (0. 6^{0.6}) + lo g_{2} (0. 4^{0.4}) = lo g_{2} (0. 6^{0.6} \cdot 0. 4^{0.4})

= - lo g_{2} (0. 6^{0.6} \cdot 0. 4^{0.4})

0. 6^{0.6} \cdot 0. 4^{0.4} = 0.51016 \dots

= - lo g_{2} (0.51016 \dots)

s im pl i f y ln (\frac{153.5}{100}) + (\frac{1}{2} \cdot 0. 4^{2} - 0.02) \cdot 4

s im pl i f y - lo g_{10} (3.75 \cdot 1 0^{2})

s im pl i f y 3 ln (x) - 2 ln (c)

s im pl i f y lo g_{10} (\frac{1}{e})

s im pl i f y 3 lo g_{10} (x) + 4 lo g_{10} (x - 2)