What is the answer to 3^x+3^{2x}=3^{3x} ?

The answer to 3^x+3^{2x}=3^{3x} is x=(ln((1+sqrt(5))/2))/(ln(3))

Solve for x: 3^x+3^{2x}=3^{3x}

The solution is x=(ln((1+sqrt(5))/2))/(ln(3))

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3^{x} + 3^{2 x} = 3^{3 x}

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( 3 )}

Decimal

x = 0.43801 \dots

Solution steps

3^{x} + 3^{2 x} = 3^{3 x}

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

u + (u)^{2} = (u)^{3}

Solve

u + u^{2} = u^{3} : u = 0, u = \frac{1 + 5}{2}, u = \frac{1 - 5}{2}

u = 0, u = \frac{1 + 5}{2}, u = \frac{1 - 5}{2}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 0 :

No Solution for

x \in R

Solve

3^{x} = \frac{1 + 5}{2} : x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( 3 )}

Solve

3^{x} = \frac{1 - 5}{2} :

No Solution for

x \in R

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( 3 )}

a (21) = 12000 (1 + (\frac{0.095}{12}))^{12 x^{21}}

4^{x} + 1 + 4^{x} = 24

3^{x + 2} - 3^{x - 2} = 2160

\frac{( 1 0 ^{4} )}{( 18.7 + 20.2 e ^{- 0.04 t} )} = 439000

((32)^{0.5})^{x} = 16

What is the answer to 3^x+3^{2x}=3^{3x} ?
The answer to 3^x+3^{2x}=3^{3x} is x=(ln((1+sqrt(5))/2))/(ln(3))
Solve for x: 3^x+3^{2x}=3^{3x}
The solution is x=(ln((1+sqrt(5))/2))/(ln(3))