Ansatz für exponential und Logarithmus

Question

Hey wie kriege ich das raus? 

lnx=3,40

ln(1-2x) = -5

0,5e^x=10

3e^x-1=5

Answer 1

ln (x)=3,40 | e hoch

x= e^3.4

x ≈ 29.964

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3e^x -1=5 | +1

3e^x = 6 |:3

e^x = 2 | ln(..)

x= ln(2)

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ln(1-2x) = -5  ; z= 1-2x

ln(z)= -5 |e hoch

z= e^-5

Rücksubstitution:

1-2x =e^-5 |-1

-2x =e^-5 -1 |.(-1)

2x =-e^-5 +1

x= (-e^-5 +1)/2

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0.5e^x=10 |:0.5

e^x= 20

x=ln(20)