What is the answer to 3^{2x}-12\times 3^x+27=0 ?

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

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3^{2x}-12\times 3^x+27=0

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

x = 2, x = 1

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

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

Solve

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

u = 9, u = 3

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 9 : x = 2

Solve

3^{x} = 3 : x = 1

x = 2, x = 1

2 (5^{3 x}) = 31250

9^{9 x + 4} = 243

4^{x + 1} + 4^{x + 2} = 320

2^{3 x - 7} = 5^{x - 4}

6 4^{x - 4} = 1 6^{x - 3}

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