What is the answer to -3^x-9(3^{-x})+10=0 ?

The answer to -3^x-9(3^{-x})+10=0 is x=0,x=2

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-3^x-9(3^{-x})+10=0

- 3^{x} - 9 (3^{- x}) + 10 = 0

x = 0, x = 2

Solution steps

- 3^{x} - 9 (3^{- x}) + 10 = 0

Apply exponent rules

- 3^{x} - 9 (3^{x})^{- 1} + 10 = 0

Rewrite the equation with

3^{x} = u

- u - 9 (u)^{- 1} + 10 = 0

Solve

- u - 9 u^{- 1} + 10 = 0 : u = 1, u = 9

u = 1, u = 9

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 1 : x = 0

Solve

3^{x} = 9 : x = 2

x = 0, x = 2

8^{x} - 8^{- x} = 8

2^{2 x + 1} 0. 4^{3 x + 1} = 8^{x - 1}

1 0^{2 x} = 4

1 0^{2 x} = 5

1 0^{2 x} = 8

What is the answer to -3^x-9(3^{-x})+10=0 ?
The answer to -3^x-9(3^{-x})+10=0 is x=0,x=2
Solve for x: -3^x-9(3^{-x})+10=0
The solution is x=0,x=2