Question

Question #6d75a

Answer 1

`x =1`

Explanation:

`e = (e^(3 x))(1/e^2)`

`e * e^2 = e^(3 x)`

`e^3 = e^(3 x)`

therefore,
`3 = 3 x`
`3/3 = x`
`1 = x`

Answer 2

(Solving the equation written in the title of this question):
`color(darkgreen)(e=e^(3x)*(1/(e^2)))`

`e=(e^(3x))(e^(-2))`

`e=e^(3x-2)`

`3x-2=1`

`3x=3`

`color(darkgreen)(x=1)`
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(Solving the equation written in the description of this question):
`color(darkblue)((e^(x^2)=e^(3x)*(1/(e^2)))`

`e^(x^2)=e^(3x-2)`

`x^2=3x-2`

`x^2-3x+2=0`
`x^2-x-2x+2=0`
`(x-2)(x-1)=0`

`color(darkblue)(x=2,x=1)`