vereinfachen 10log_{10}(0.1((0.125)/(4pi8))^2)

Lösung

vereinfachen

10 \cdot lo g_{10} (0.1 \cdot (\frac{0.125}{4 \cdot π \cdot 8})^{2})

10 lo g_{10} (0.1) + 20 lo g_{10} (\frac{0.125}{32 π})

Dezimale

- 68.10779 \dots

Schritte zur Lösung

10 lo g_{10} (0.1 (\frac{0.125}{4 π 8})^{2})

Wende die log Regel an:

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

10 lo g_{10} (0.1 (\frac{0.125}{4 π 8})^{2}) = 10 lo g_{10} (0.1) + 10 lo g_{10} ((\frac{0.125}{4 π 8})^{2})

= 10 lo g_{10} (0.1) + 10 lo g_{10} ((\frac{0.125}{4 \cdot 8 π})^{2})

Wende die log Regel an:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} ((\frac{0.125}{4 π 8})^{2}) = 2 lo g_{10} (\frac{0.125}{4 π 8})

= 10 lo g_{10} (0.1) + 10 \cdot 2 lo g_{10} (\frac{0.125}{4 π 8})

10 \cdot 2 lo g_{10} (\frac{0.125}{4 π 8}) = 20 lo g_{10} (\frac{0.125}{32 π})

= 10 lo g_{10} (0.1) + 20 lo g_{10} (\frac{0.125}{32 π})

s im pl i f y ln (\frac{1}{2}) \cdot ln (\frac{1}{2})

s im pl i f y ln (\frac{n !}{x ^{n + 1}})

s im pl i f y ln (\frac{x ^{2}}{sin ^{3} ( x )})

s im pl i f y - 0.1 ln (0.1) - (1 - 0.1) ln (1 - 0.1)

s im pl i f y - ln (2) + ln (3) + \frac{3}{2} ln (2)