What is the answer to x=0.9894+7^{x-1} ?

The answer to x=0.9894+7^{x-1} is No Solution for x\in\mathbb{R}

Solve for x: x=0.9894+7^{x-1}

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

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x = 0.9894 + 7^{x - 1}

No Solution for x \in R

Solution steps

x = 0.9894 + 7^{x - 1}

Prepare

x = 0.9894 + 7^{x - 1}

for Lambert form:

1 = (x - 0.9894) e^{l n (7) (- x + 1)}

Rewrite the equation with

(- x + 0.9894) ln (7) = u

and

x = - \frac{u}{ln ( 7 )} + 0.9894

1 = ((- \frac{u}{ln ( 7 )} + 0.9894) - 0.9894) e^{l n (7) (- (- \frac{u}{l n ( 7 )} + 0.9894) + 1)}

Simplify

1 = - \frac{e ^{u + 0.0106 l n (7)} u}{ln ( 7 )}

Rewrite

1 = - \frac{e ^{u + 0.0106 l n (7)} u}{ln ( 7 )}

in Lambert form:

e^{u} u = - \frac{ln ( 7 )}{7 ^{0.0106}}

Solve

e^{u} u = - \frac{ln ( 7 )}{7 ^{0.0106}} :

No Solution for

u \in R

No Solution for x \in R

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(2 x + 4)^{5 - x} = (2 x + 4)^{3 - 2 x}

e^{x} = 0.4

e^{l n (3 x)} = 11

40000 = 2^{t} \cdot 100

What is the answer to x=0.9894+7^{x-1} ?
The answer to x=0.9894+7^{x-1} is No Solution for x\in\mathbb{R}
Solve for x: x=0.9894+7^{x-1}
The solution is No Solution for x\in\mathbb{R}