What is the answer to x^5=9^x ?

The answer to x^5=9^x is No Solution for x\in\mathbb{R}

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

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x^5=9^x

x^{5} = 9^{x}

No Solution for x \in R

Solution steps

x^{5} = 9^{x}

Prepare

x^{5} = 9^{x}

for Lambert form:

x e^{- \frac{2 l n ( 3 ) x}{5}} = 1

Rewrite the equation with

- \frac{2 ln ( 3 ) x}{5} = u

and

x = - \frac{5 u}{2 ln ( 3 )}

(- \frac{5 u}{2 ln ( 3 )}) e^{u} = 1

Rewrite

(- \frac{5 u}{2 ln ( 3 )}) e^{u} = 1

in Lambert form:

e^{u} u = - \frac{2 ln ( 3 )}{5}

Solve

e^{u} u = - \frac{2 ln ( 3 )}{5} :

No Solution for

u \in R

No Solution for x \in R

6 e^{x} - 4 e^{- x} = 5

T, x^{T} A^{T} A x = 0

e^{4 x} = 8 e^{x}

8^{4 x + 1} = 1

2 e^{6 x} = 13

What is the answer to x^5=9^x ?
The answer to x^5=9^x is No Solution for x\in\mathbb{R}
Solve for x: x^5=9^x
The solution is No Solution for x\in\mathbb{R}