What is the answer to 27(3^{2x})-12(3^x)+1=0 ?

The answer to 27(3^{2x})-12(3^x)+1=0 is x=-1,x=-2

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27(3^{2x})-12(3^x)+1=0

27 (3^{2 x}) - 12 (3^{x}) + 1 = 0

x = - 1, x = - 2

Solution steps

27 (3^{2 x}) - 12 (3^{x}) + 1 = 0

Apply exponent rules

27 (3^{x})^{2} - 12 \cdot 3^{x} + 1 = 0

Rewrite the equation with

3^{x} = u

27 (u)^{2} - 12 u + 1 = 0

Solve

27 u^{2} - 12 u + 1 = 0 : u = \frac{1}{3}, u = \frac{1}{9}

u = \frac{1}{3}, u = \frac{1}{9}

Substitute back

u = 3^{x},

solve for

x

Solve

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

Solve

3^{x} = \frac{1}{9} : x = - 2

x = - 1, x = - 2

8^{x} = \frac{2 ^{32} - 4 ^{14}}{30}

x = e^{- x} - 2

7^{3 x - 2} = 1

(2 e^{3 x})^{3} = 9

2^{2 x} - 2^{x + 2} = 32

What is the answer to 27(3^{2x})-12(3^x)+1=0 ?
The answer to 27(3^{2x})-12(3^x)+1=0 is x=-1,x=-2
Solve for x: 27(3^{2x})-12(3^x)+1=0
The solution is x=-1,x=-2