Forme jeweils auf die angegebene Variable um

Question

Aufgabe:

a) ΔT=1-(a₁/a₂)•ln(t+1)

t=?

b) b•(1-ln(a/t))=r₁/r₂

t=?

Problem/Ansatz:

Answer 1

ΔT=1-(a1/a2)•ln(t+1)

(a1/a2)•ln(t+1) = 1 - ΔT

ln(t+1) = (1 - ΔT)•(a2/a1)

t+1 = e^( (1 - ΔT)•(a2/a1))

t = e^( (1 - ΔT)•(a2/a1)) - 1

b•(1-ln(a/t))=r1/r2

1-ln(a/t)=r1/(r2•b)

1-ln(a) + ln(t)=r1/(r2•b)

ln(t)=r1/(r2•b)-1 + ln(a) 

t = e^(r1/(r2•b)-1 + ln(a) ) = e^(r1/(r2•b))  • a/e