I cant find the error: e^{pi*x} = -1 leads to x = 0 ??

[And]

https://ibb.co/eMvKgQ:

Given: \(\displaystyle e^{\pi x}\, =\, -1\)

Then:

. . . . .\(\displaystyle \left(e^{\pi x}\right)^2\, =\, (-1)^2\)

. . . . .\(\displaystyle e^{2\pi x}\, =\, 1\)

. . . . .\(\displaystyle e^{2\pi x}\, =\, e^0\)

. . . . .\(\displaystyle 2\pi x \, =\, 0\)

. . . . .\(\displaystyle x\, =\, 0\)

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I cant find the error of this ecquation

 

[mmm4444bot]

I cant find the error of this [equation]

e^(Pi*x) = -1

When solving an equation, squaring both sides can sometimes introduce false solutions. We call these "extraneous solutions".

This is why we must always verify results, when we have squared both sides of an equation.

That equation has a solution; try taking the natural log of each side, to start. :cool: