What is the answer to x^4=4^x ?

The answer to x^4=4^x is x=-(2\W_{0}((ln(2))/2))/(ln(2)),x=2,x=4

The solution is x=-(2\W_{0}((ln(2))/2))/(ln(2)),x=2,x=4

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x^4=4^x

x^{4} = 4^{x}

x = - \frac{2 W _{0} ( \frac{l n ( 2 )}{2} )}{ln ( 2 )}, x = 2, x = 4

Decimal Notation

x = - 0.76666 \dots, x = 2, x = 4

Solution steps

x^{4} = 4^{x}

Take both sides of the equation to the power of

\frac{1}{4}

(x^{4})^{\frac{1}{4}} = (4^{x})^{\frac{1}{4}}

Simplify

(x^{4})^{\frac{1}{4}} : ∣ x ∣

Simplify

(4^{x})^{\frac{1}{4}} : 2^{\frac{x}{2}}

Solve

∣ x ∣ = 2^{\frac{x}{2}} : x = - \frac{2 W _{0} ( \frac{l n ( 2 )}{2} )}{ln ( 2 )} or x = 2 or x = 4

x = - \frac{2 W _{0} ( \frac{l n ( 2 )}{2} )}{ln ( 2 )}, x = 2, x = 4

1 1^{2 x^{2} - 5 x + 2} = 1

(\frac{1}{125})^{x} = 25

5 e^{2 x + 11} = 30

2^{3 x + 7} - 9 = 17

x^{x^{5}} = 5

What is the answer to x^4=4^x ?
The answer to x^4=4^x is x=-(2\W_{0}((ln(2))/2))/(ln(2)),x=2,x=4
Solve for x: x^4=4^x
The solution is x=-(2\W_{0}((ln(2))/2))/(ln(2)),x=2,x=4