What is the answer to 2x=8^x+4 ?

The answer to 2x=8^x+4 is No Solution for x\in\mathbb{R}

Solve for x: 2x=8^x+4

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

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2 x = 8^{x} + 4

No Solution for x \in R

Solution steps

2 x = 8^{x} + 4

Prepare

2 x = 8^{x} + 4

for Lambert form:

1 = (2 x - 4) e^{- 3 l n (2) x}

Rewrite the equation with

3 ln (2) (- x + 2) = u

and

x = - \frac{u - 6 ln ( 2 )}{3 ln ( 2 )}

1 = (2 (- \frac{u - 6 ln ( 2 )}{3 ln ( 2 )}) - 4) e^{- 3 l n (2) (- \frac{u - 6 l n ( 2 )}{3 l n ( 2 )})}

Simplify

1 = e^{u - 6 l n (2)} (- \frac{2 ( u - 6 ln ( 2 ) )}{3 ln ( 2 )} - 4)

Rewrite

1 = e^{u - 6 l n (2)} (- \frac{2 ( u - 6 ln ( 2 ) )}{3 ln ( 2 )} - 4)

in Lambert form:

e^{u} u = - 96 ln (2)

Solve

e^{u} u = - 96 ln (2) :

No Solution for

u \in R

No Solution for x \in R

3^{- 4 x} = 9^{6 - x}

4^{2 n + 1} - 12 = 52

2^{x} = 512

5 e^{x} = 36

1024 = 2^{5 x}

What is the answer to 2x=8^x+4 ?
The answer to 2x=8^x+4 is No Solution for x\in\mathbb{R}
Solve for x: 2x=8^x+4
The solution is No Solution for x\in\mathbb{R}