What is the answer to x/((1/2))=2^x+3 ?

The answer to x/((1/2))=2^x+3 is No Solution for x\in\mathbb{R}

Solve for x: x/((1/2))=2^x+3

The solution is No Solution for x\in\mathbb{R}

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\frac{x}{( \frac{1}{2} )} = 2^{x} + 3

No Solution for x \in R

Solution steps

\frac{x}{( \frac{1}{2} )} = 2^{x} + 3

Prepare

\frac{x}{( \frac{1}{2} )} = 2^{x} + 3

for Lambert form:

\frac{1}{2} = (x - \frac{3}{2}) e^{- l n (2) x}

Rewrite the equation with

(- x + \frac{3}{2}) ln (2) = u

and

x = - \frac{2 u - 3 ln ( 2 )}{2 ln ( 2 )}

\frac{1}{2} = ((- \frac{2 u - 3 ln ( 2 )}{2 ln ( 2 )}) - \frac{3}{2}) e^{- l n (2) (- \frac{2 u - 3 l n ( 2 )}{2 l n ( 2 )})}

Simplify

\frac{1}{2} = - \frac{e ^{\frac{2 u - 3 l n ( 2 )}{2}} u}{ln ( 2 )}

Rewrite

\frac{1}{2} = - \frac{e ^{\frac{2 u - 3 l n ( 2 )}{2}} u}{ln ( 2 )}

in Lambert form:

e^{u} u = - \frac{e ^{\frac{3 l n ( 2 )}{2}} ln ( 2 )}{2}

Solve

e^{u} u = - \frac{e ^{\frac{3 l n ( 2 )}{2}} ln ( 2 )}{2} :

No Solution for

u \in R

No Solution for x \in R

(\frac{2}{5})^{3 x - 7} = (\frac{5}{2})^{7 x - 3}

e^{x} + e^{- x} = 2

2^{n - 1} + 2^{n + 1} = 320

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

1 0^{x - 1} = 1000

What is the answer to x/((1/2))=2^x+3 ?
The answer to x/((1/2))=2^x+3 is No Solution for x\in\mathbb{R}
Solve for x: x/((1/2))=2^x+3
The solution is No Solution for x\in\mathbb{R}