What is the answer to 3^x=x^2 ?

The answer to 3^x=x^2 is x=-(2\W_{0}((ln(3))/2))/(ln(3))

The solution is x=-(2\W_{0}((ln(3))/2))/(ln(3))

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3^x=x^2

3^{x} = x^{2}

x = - \frac{2 W _{0} ( \frac{l n ( 3 )}{2} )}{ln ( 3 )}

Decimal Notation

x = - 0.68602 \dots

Solution steps

3^{x} = x^{2}

Take both sides of the equation to the power of

\frac{1}{2}

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

Simplify

(3^{x})^{\frac{1}{2}} : 3^{\frac{x}{2}}

Simplify

(x^{2})^{\frac{1}{2}} : ∣ x ∣

Solve

3^{\frac{x}{2}} = ∣ x ∣ : x = - \frac{2 W _{0} ( \frac{l n ( 3 )}{2} )}{ln ( 3 )}

x = - \frac{2 W _{0} ( \frac{l n ( 3 )}{2} )}{ln ( 3 )}

5 \cdot 1 0^{\frac{z}{4}} = 32

3^{2 x + 1} + 3 = 10 \cdot 3^{x}

e^{3 x + 1} = 100

5 = 6^{x}

ln (e^{x}) = 1

What is the answer to 3^x=x^2 ?
The answer to 3^x=x^2 is x=-(2\W_{0}((ln(3))/2))/(ln(3))
Solve for x: 3^x=x^2
The solution is x=-(2\W_{0}((ln(3))/2))/(ln(3))