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

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

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3^x+3^{(3-x)}=12

3^{x} + 3^{(3 - x)} = 12

x = 2, x = 1

Solution steps

3^{x} + 3^{(3 - x)} = 12

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

u + (u)^{- 1} \cdot 3^{3} = 12

Solve

u + u^{- 1} \cdot 3^{3} = 12 : 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

8^{- x} = \frac{1}{2}

7^{x} = \frac{1}{49}

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

4^{2 x} = 64

x^{l o g_{3} (x)} = 81

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