What is the answer to 9^x=12*3^x-27 ?

The answer to 9^x=12*3^x-27 is x=2,x=1

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9^x=12*3^x-27

9^{x} = 12 \cdot 3^{x} - 27

x = 2, x = 1

Solution steps

9^{x} = 12 \cdot 3^{x} - 27

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

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

Solve

u^{2} = 12 u - 27 : 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^{x} = 2 x

2^{x} = 81

2^{x} = 29

4 (8^{x}) = 64

(\frac{1}{2})^{x - 1} = 2^{3 x - 4}