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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^2=3^x

x^{2} = 3^{x}

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

Decimal Notation

x = - 0.68602 \dots

Solution steps

x^{2} = 3^{x}

Take both sides of the equation to the power of

\frac{1}{2}

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

Simplify

(x^{2})^{\frac{1}{2}} : ∣ x ∣

Simplify

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

Solve

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

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

6^{x^{2} + 4 x - 63} = 3 6^{4 x - 9}

(\frac{1}{5})^{x} = 125

e^{- x} - x = 0

3 (3^{x}) + 9 (3^{- x}) = 28

2 \cdot 9^{x} = 162

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