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

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

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3^x-12+27*3^{-x}=0

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

x = 2, x = 1

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

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

Solve

u - 12 + 27 u^{- 1} = 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

9^{4 x} = \frac{1}{27}

3^{x^{2}} \cdot 3 = 3

7^{2 x - 1} = 295

e^{x} - 1 = 6

(\frac{2}{4})^{3 x} = 64

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