What is the answer to 3^x-3^{2-x}=8 ?

The answer to 3^x-3^{2-x}=8 is x=2

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3^x-3^{2-x}=8

3^{x} - 3^{2 - x} = 8

x = 2

Solution steps

3^{x} - 3^{2 - x} = 8

Apply exponent rules

3^{x} - (3^{x})^{- 1} \cdot 3^{2} = 8

Rewrite the equation with

3^{x} = u

u - (u)^{- 1} \cdot 3^{2} = 8

Solve

u - u^{- 1} \cdot 3^{2} = 8 : u = 9, u = - 1

u = 9, u = - 1

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 9 : x = 2

Solve

3^{x} = - 1 :

No Solution for

x \in R

x = 2

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lo g_{3} (x^{l o g_{3} (x)}) = 4

1050 = 480 e^{7 r}

5^{x} + 5^{x + 1} - \frac{6}{25} = 0

2^{x + 1} + 2^{x} + 2^{x - 1} = 14