What is the answer to 2^{ea}=a ?

The answer to 2^{ea}=a is No Solution for a\in\mathbb{R}

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2^{ea}=a

2^{e a} = a

No Solution for a \in R

Solution steps

2^{e a} = a

Prepare

2^{e a} = a

for Lambert form:

1 = a e^{- e l n (2) a}

Rewrite the equation with

- e a ln (2) = u

and

a = - \frac{u}{e ln ( 2 )}

1 = (- \frac{u}{e ln ( 2 )}) e^{u}

Rewrite

1 = (- \frac{u}{e ln ( 2 )}) e^{u}

in Lambert form:

e^{u} u = - e ln (2)

Solve

e^{u} u = - e ln (2) :

No Solution for

u \in R

No Solution for a \in R

100 = 96.87 e^{r}

7^{2 x + 1} - 4 9^{x} = 42

9^{x} = 2 \cdot 3^{x} + 3

3 \cdot 2^{x - 1} - 1 = 2

1 3^{- 7 x} - 8 = 85

What is the answer to 2^{ea}=a ?
The answer to 2^{ea}=a is No Solution for a\in\mathbb{R}