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

The answer to 2^x=x^4 is x=-(4\W_{0}((ln(2))/4))/(ln(2)),x=-(4\W_{0}(-(ln(2))/4))/(ln(2)),x=16

The solution is x=-(4\W_{0}((ln(2))/4))/(ln(2)),x=-(4\W_{0}(-(ln(2))/4))/(ln(2)),x=16

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2^x=x^4

2^{x} = x^{4}

x = - \frac{4 W _{0} ( \frac{l n ( 2 )}{4} )}{ln ( 2 )}, x = - \frac{4 W _{0} ( - \frac{l n ( 2 )}{4} )}{ln ( 2 )}, x = 16

Decimal Notation

x = - 0.86134 \dots, x = 1.23962 \dots, x = 16

Solution steps

2^{x} = x^{4}

Take both sides of the equation to the power of

\frac{1}{4}

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

Simplify

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

Simplify

(x^{4})^{\frac{1}{4}} : ∣ x ∣

Solve

2^{\frac{x}{4}} = ∣ x ∣ : x = - \frac{4 W _{0} ( \frac{l n ( 2 )}{4} )}{ln ( 2 )} or x = - \frac{4 W _{0} ( - \frac{l n ( 2 )}{4} )}{ln ( 2 )} or x = 16

x = - \frac{4 W _{0} ( \frac{l n ( 2 )}{4} )}{ln ( 2 )}, x = - \frac{4 W _{0} ( - \frac{l n ( 2 )}{4} )}{ln ( 2 )}, x = 16

1.2 5^{x} = 0.512

(- 3)^{x - 1} = 729

(\frac{1}{2 ^{x - 4}}) - (\frac{1}{2 ^{x - 2}}) = 3

4^{2} x + 8 = 3 (8^{x})

4^{x} = 64

What is the answer to 2^x=x^4 ?
The answer to 2^x=x^4 is x=-(4\W_{0}((ln(2))/4))/(ln(2)),x=-(4\W_{0}(-(ln(2))/4))/(ln(2)),x=16
Solve for x: 2^x=x^4
The solution is x=-(4\W_{0}((ln(2))/4))/(ln(2)),x=-(4\W_{0}(-(ln(2))/4))/(ln(2)),x=16