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Question

Zwei Gleichungen : e^3x(e^x)^2 = Wurzel( e^-8/e^2x) Und In(wurzel(7^{12-x}) + 11ln2 = 11ln16

Answer 1

Hi,

e^{3x}(e^x)^2 = √(e^{-8}/e^{2x})

e^{3x}e^{2x} = √e^{-2x-8}

e^{3x+2x} = e^{-x-4}

e^{5x} = e^{-x-4}

5x = -x-4   |+x

6x = -4

x = -2/3

 

ln(√(7^{12-x}) + 11ln(2) = 11ln(6)

ln(7^(12-x)/2) + 11ln(2) = 11ln(2) + 11ln(3)   |-11ln(2)

ln(7^(12-x)/2) = 11ln(3)

(12-x)/2 ln(7) = 11ln(3)

6ln(7) - x/2*ln(7) = 11ln(3)    |-11ln(3)+x/2ln(7)

x/2 ln(7) = 6ln(7) - 11ln(3)

x = 2(6ln(7)-11ln(3))/ln(7) ≈ -0,42

 

Alles klar?

Grüße