What is the answer to 5^x-5^{-x}=8 ?

The answer to 5^x-5^{-x}=8 is x=(ln(4+sqrt(17)))/(ln(5))

Solve for x: 5^x-5^{-x}=8

The solution is x=(ln(4+sqrt(17)))/(ln(5))

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5^{x} - 5^{- x} = 8

x = \frac{ln ( 4 + 17 )}{ln ( 5 )}

Decimal Notation

x = 1.30151 \dots

Solution steps

5^{x} - 5^{- x} = 8

Apply exponent rules

5^{x} - (5^{x})^{- 1} = 8

Rewrite the equation with

5^{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 = 5^{x},

solve for

x

Solve

5^{x} = 4 + 17 : x = \frac{ln ( 4 + 17 )}{ln ( 5 )}

Solve

5^{x} = 4 - 17 :

No Solution for

x \in R

x = \frac{ln ( 4 + 17 )}{ln ( 5 )}

6^{x - 1} = 8^{2 - x}

6^{3 x + 2} = 3 6^{x - 6}

2 (5^{x}) = 32

2^{2 x + 2} = 2^{3 x}

e^{2 x} - 12 e^{x} + 11 = 0

What is the answer to 5^x-5^{-x}=8 ?
The answer to 5^x-5^{-x}=8 is x=(ln(4+sqrt(17)))/(ln(5))
Solve for x: 5^x-5^{-x}=8
The solution is x=(ln(4+sqrt(17)))/(ln(5))