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

The answer to 8^x-8^{-x}=8 is x=(ln(4+sqrt(17)))/(3ln(2))

Solve for x: 8^x-8^{-x}=8

The solution is x=(ln(4+sqrt(17)))/(3ln(2))

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

x = \frac{ln ( 4 + 17 )}{3 ln ( 2 )}

Solution steps

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

Apply exponent rules

8^{x} - (8^{x})^{- 1} = 8

Rewrite the equation with

8^{x} = u

u - (u)^{- 1} = 8

Solve

u - u^{- 1} = 8 : u = 4 + 17, u = 4 - 17

u = 4 + 17, u = 4 - 17

Substitute back

u = 8^{x},

solve for

x

Solve

8^{x} = 4 + 17 : x = \frac{ln ( 4 + 17 )}{3 ln ( 2 )}

Solve

8^{x} = 4 - 17 :

No Solution for

x \in R

x = \frac{ln ( 4 + 17 )}{3 ln ( 2 )}

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

9^{x + 1} = 2 7^{5 x - 5}

What is the answer to 8^x-8^{-x}=8 ?
The answer to 8^x-8^{-x}=8 is x=(ln(4+sqrt(17)))/(3ln(2))
Solve for x: 8^x-8^{-x}=8
The solution is x=(ln(4+sqrt(17)))/(3ln(2))