`e^(-4x) lt= 9` Solve for x.

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lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on


To solve, take the natural logarithm of both sides of the equation.

`ln e^(-4x)lt=ln9`

At the left side, apply the exponent property of logarithm which is  `ln a^m=m ln a` .

`-4x ln elt=ln 9`

Note that `ln e =1` .  So,

`-4x(1)lt= ln 9`

`-4xlt= ln 9`

Then, divide both sides by -4 to isolate the x.

`(-4x)/(-4) lt= ln9/(-4)`

Since the sign of x changes, the inequality changes too.

`x gt= -ln9/4`

Hence, the solution to the given equation is `xgt=-ln9/4` .

oldnick's profile pic

oldnick | (Level 1) Valedictorian

Posted on


Since function `e^(-4x) `  is an one -to-one function, then we can use logartitms:

`-4x<=ln 9` 

`x>= -1/4 ln9`  for inequality  properties.




Let you see, the value we are searchinfg for , run from the point of graphic  with the straight line `y=9`  to the right side on. The relative point ,is about  `x=-0.54`

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