What is the answer to 3^{2x}-6*3^x+8=0 ?

The answer to 3^{2x}-6*3^x+8=0 is x=(2ln(2))/(ln(3)),x=(ln(2))/(ln(3))

Solve for x: 3^{2x}-6*3^x+8=0

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

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3^{2 x} - 6 \cdot 3^{x} + 8 = 0

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

Decimal Notation

x = 1.26185 \dots, x = 0.63092 \dots

Solution steps

3^{2 x} - 6 \cdot 3^{x} + 8 = 0

Apply exponent rules

(3^{x})^{2} - 6 \cdot 3^{x} + 8 = 0

Rewrite the equation with

3^{x} = u

(u)^{2} - 6 u + 8 = 0

Solve

u^{2} - 6 u + 8 = 0 : u = 4, u = 2

u = 4, u = 2

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 4 : x = \frac{2 ln ( 2 )}{ln ( 3 )}

Solve

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

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

22.33 = 16 + 5 4^{- k (25)}

7^{4 x} = 49

t, 0.1 = 50 (0. 9^{t})

3 e^{x} = 120

4 = 8^{x}

What is the answer to 3^{2x}-6*3^x+8=0 ?
The answer to 3^{2x}-6*3^x+8=0 is x=(2ln(2))/(ln(3)),x=(ln(2))/(ln(3))
Solve for x: 3^{2x}-6*3^x+8=0
The solution is x=(2ln(2))/(ln(3)),x=(ln(2))/(ln(3))