What is the answer to 3^{2x+1}-4(3^{3x+1})+1=0 ?

The answer to 3^{2x+1}-4(3^{3x+1})+1=0 is x=-0.56432…

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3^{2x+1}-4(3^{3x+1})+1=0

3^{2 x + 1} - 4 (3^{3 x + 1}) + 1 = 0

x = - 0.56432 \dots

Solution steps

3^{2 x + 1} - 4 (3^{3 x + 1}) + 1 = 0

Apply exponent rules

(3^{x})^{2} \cdot 3^{1} - 4 (3^{x})^{3} \cdot 3^{1} + 1 = 0

Rewrite the equation with

3^{x} = u

(u)^{2} \cdot 3^{1} - 4 (u)^{3} \cdot 3^{1} + 1 = 0

Solve

u^{2} \cdot 3^{1} - 4 u^{3} \cdot 3^{1} + 1 = 0 : u \approx 0.53795 \dots

u \approx 0.53795 \dots

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 0.53795 \dots : x = - 0.56432 \dots

x = - 0.56432 \dots

1 0^{x} = 10

1 0^{x} = 24

1 0^{x} = 30

x \cdot e^{x} = 1

8^{3 x - 1} = 4^{3 - 2 x}

What is the answer to 3^{2x+1}-4(3^{3x+1})+1=0 ?
The answer to 3^{2x+1}-4(3^{3x+1})+1=0 is x=-0.56432…
Solve for x: 3^{2x+1}-4(3^{3x+1})+1=0
The solution is x=-0.56432…