If e^-x=4 , then find the value of x
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answer is b option.
Taking natural log on both sides we get-
![log_{e}(e ^{ - x} ) = log_{e}(4) log_{e}(e ^{ - x} ) = log_{e}(4)](https://tex.z-dn.net/?f=+log_%7Be%7D%28e+%5E%7B+-+x%7D+%29++%3D++log_%7Be%7D%284%29+)
it simplifies to-
![- x log_{e}(e) = log_{e}(4) - x log_{e}(e) = log_{e}(4)](https://tex.z-dn.net/?f=+-+x+log_%7Be%7D%28e%29+%3D++log_%7Be%7D%284%29++)
therefore,
![x = - log_{e}(4) x = - log_{e}(4)](https://tex.z-dn.net/?f=x+%3D++-++log_%7Be%7D%284%29+)
Taking natural log on both sides we get-
it simplifies to-
therefore,
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