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To solve, take the natural logarithm of both sides of the equation.
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` .
Since function `e^(-4x) ` is an one -to-one function, then we can use logartitms:
`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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