What is the answer to (e^x-1)/x =1 ?

The answer to (e^x-1)/x =1 is No Solution for x\in\mathbb{R}

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(e^x-1)/x =1

\frac{e ^{x} - 1}{x} = 1

No Solution for x \in R

Solution steps

\frac{e ^{x} - 1}{x} = 1

Prepare

\frac{e ^{x} - 1}{x} = 1

for Lambert form:

1 = (x + 1) e^{- x}

Rewrite the equation with

- x - 1 = u

and

x = - u - 1

1 = ((- u - 1) + 1) e^{- (- u - 1)}

Simplify

1 = - e^{u + 1} u

Rewrite

1 = - e^{u + 1} u

in Lambert form:

e^{u} u = - \frac{1}{e}

Solve

e^{u} u = - \frac{1}{e} : u = - 1

u = - 1

Substitute back

u = - x - 1,

solve for

x

Solve

- x - 1 = - 1 : x = 0

x = 0

Verify Solutions:

x = 0

False

The solution is

No Solution for x \in R

3^{x} - 9^{2 x} = 2 7^{3 x}

7^{2 x - 6} = 1

3 6^{x} = \frac{1}{6}

9^{x + 1} = 2 7^{2 x - 3}

4^{x} = e^{x + 5}

What is the answer to (e^x-1)/x =1 ?
The answer to (e^x-1)/x =1 is No Solution for x\in\mathbb{R}