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Question

2ln(5-e^-2x)=1?

Answer 1

The natural logarithmic equation is 2ln(5-e^-2x )=1.

Divide each side by 2.

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

If lna = b then e^b = a.

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

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

If e^b = a, then lna = b where a = 5 - e^(1/2) and b = -2x.

 

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

x = (-1/2) ln (5 - e^(1/2))          [ 5 - e^(1/2) = 3.3513]

 

x = (-1/2) ln (3.3513)

 

x = (-1/2) (1.2093)

 

x = -0.60467 (rounded).