What is the answer to 3^{2x}-3^{x+2}+8=0 ?

The answer to 3^{2x}-3^{x+2}+8=0 is x=(3ln(2))/(ln(3)),x=0

Solve for x: 3^{2x}-3^{x+2}+8=0

The solution is x=(3ln(2))/(ln(3)),x=0

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3^{2 x} - 3^{x + 2} + 8 = 0

x = \frac{3 ln ( 2 )}{ln ( 3 )}, x = 0

Decimal

x = 1.89278 \dots, x = 0

Solution steps

3^{2 x} - 3^{x + 2} + 8 = 0

Apply exponent rules

(3^{x})^{2} - 3^{x} \cdot 3^{2} + 8 = 0

Rewrite the equation with

3^{x} = u

(u)^{2} - u \cdot 3^{2} + 8 = 0

Solve

u^{2} - u \cdot 3^{2} + 8 = 0 : u = 8, u = 1

u = 8, u = 1

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 8 : x = \frac{3 ln ( 2 )}{ln ( 3 )}

Solve

3^{x} = 1 : x = 0

x = \frac{3 ln ( 2 )}{ln ( 3 )}, x = 0

e^{- 2 t} - 4 \cdot e^{- t} + 4 = 0

4^{- 3 v} = 64

3^{2 x + 1} + 3^{x} - 2 = 0

2^{- 3 x} = 16

e^{y} + y = 1

What is the answer to 3^{2x}-3^{x+2}+8=0 ?
The answer to 3^{2x}-3^{x+2}+8=0 is x=(3ln(2))/(ln(3)),x=0
Solve for x: 3^{2x}-3^{x+2}+8=0
The solution is x=(3ln(2))/(ln(3)),x=0