85 = 219.37e^-0,155x. Solve x.

Question

I have this equation : 85 = 219.37e^-0,155x 
and the question is "Solve x."

Answer 1

85=219.37e^(-0.155x)

85/219.37=e^(-0.155x)

0.3874732=e^(-0.155x)

take the natural log of both sides

ln(0.3874732)=ln(e^[-0.155x])

-0.94810859387=-0.155x because ln(e^[x])=x

-0.94810859387/-0.155=x

x=6.1168296 (round off accordingly)

Answer 2

85 = 219.37e^-0.155x

 

Since we have an exponential function with number e, we want to natural log both sides of the equation, and bring the exponent of the number e as the coefficient of the natural log.

 

 

ln(85) = -0.155xln(219.37)

 

 

Divide both sides of the equation by -0.155ln(219.37).

 

ln(85) / [-0.155ln(219.37)] = x