What is the answer to 3^{2x}-6*3^x+5=0 ?

The answer to 3^{2x}-6*3^x+5=0 is x=(ln(5))/(ln(3)),x=0

Solve for x: 3^{2x}-6*3^x+5=0

The solution is x=(ln(5))/(ln(3)),x=0

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3^{2 x} - 6 \cdot 3^{x} + 5 = 0

x = \frac{ln ( 5 )}{ln ( 3 )}, x = 0

Solution steps

3^{2 x} - 6 \cdot 3^{x} + 5 = 0

Apply exponent rules

(3^{x})^{2} - 6 \cdot 3^{x} + 5 = 0

Rewrite the equation with

3^{x} = u

(u)^{2} - 6 u + 5 = 0

Solve

u^{2} - 6 u + 5 = 0 : u = 5, u = 1

u = 5, u = 1

Substitute back

u = 3^{x},

solve for

x

Solve

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

Solve

3^{x} = 1 : x = 0

x = \frac{ln ( 5 )}{ln ( 3 )}, x = 0

2^{2 x} - 2^{x + 1} - 8 = 0

(\frac{1}{64})^{- x - 3} = 16

2^{2 x - 5} = 8^{x + 7}

2 - e^{x} = 10 e^{- x} - 5

What is the answer to 3^{2x}-6*3^x+5=0 ?
The answer to 3^{2x}-6*3^x+5=0 is x=(ln(5))/(ln(3)),x=0
Solve for x: 3^{2x}-6*3^x+5=0
The solution is x=(ln(5))/(ln(3)),x=0