Beispiel: 50= -10lg(10^-5,7 + 10^ (x/10) Wie löse ich das nach x auf? Danke
Beispiel: Wie löse ich das nach x auf?
50=−10⋅log10(10(−5,7)+10(x10))50=−10⋅log10(10(−5,7)+10(x10))|:−10−5=log10[10(−5,7)+10(x10)]−5=log10[10(−5,7)+10(x10)]|:10x10−5=10(−5,7)+10(x10)10(x10)=10(−5)−10(−5,7)|log10log10(10(x10))=log10(10(−5)−10(−5,7))x10⋅log10(10)=log10(10(−5)−10(−5,7))|log10=1x10=log10(10(−5)−10(−5,7))
x=10⋅log10(10(−5)−10(−5,7))x=10⋅log10(0,00001−0,00000199526)x=10⋅log10(0,00000800474)x=10⋅−5,09665289533x=−50,9665289533
Probe:
50=−10⋅log10(10(−5,7)+10(x10))50=−10⋅log10(10(−5,7)+10(−50,966528953310))50=−10⋅log10(10(−5,7)+10(−5,09665289533))50=−10⋅log10(0,00000199526+0,00000800474)50=−10⋅log10(0,00001)50=−10⋅(−5)50=50okay
50=−(10×log10(10−5.7+10(x10))) : (-10)
−5=log10(10−5.7+10(x10)) e^x
e−5=10−5.7+10(x10) -10^-5.7
e−5−10−5.7=10(x10) log
log10(e−5−10−5.7)=(x10) *10
10×log10(e−5−10−5.7)=x
x=−21.72
.Beispiel: Wie löse ich das nach x auf?
50=−10⋅log10(10(−5,7)+10(x10))50=−10⋅log10(10(−5,7)+10(x10))|:−10−5=log10[10(−5,7)+10(x10)]−5=log10[10(−5,7)+10(x10)]|:10x10−5=10(−5,7)+10(x10)10(x10)=10(−5)−10(−5,7)|log10log10(10(x10))=log10(10(−5)−10(−5,7))x10⋅log10(10)=log10(10(−5)−10(−5,7))|log10=1x10=log10(10(−5)−10(−5,7))
x=10⋅log10(10(−5)−10(−5,7))x=10⋅log10(0,00001−0,00000199526)x=10⋅log10(0,00000800474)x=10⋅−5,09665289533x=−50,9665289533
Probe:
50=−10⋅log10(10(−5,7)+10(x10))50=−10⋅log10(10(−5,7)+10(−50,966528953310))50=−10⋅log10(10(−5,7)+10(−5,09665289533))50=−10⋅log10(0,00000199526+0,00000800474)50=−10⋅log10(0,00001)50=−10⋅(−5)50=50okay