What is the answer to 5^x-5^{-x}=2 ?

The answer to 5^x-5^{-x}=2 is x=(ln(1+sqrt(2)))/(ln(5))

Solve for x: 5^x-5^{-x}=2

The solution is x=(ln(1+sqrt(2)))/(ln(5))

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5^{x} - 5^{- x} = 2

x = \frac{ln ( 1 + 2 )}{ln ( 5 )}

Solution steps

5^{x} - 5^{- x} = 2

Apply exponent rules

5^{x} - (5^{x})^{- 1} = 2

Rewrite the equation with

5^{x} = u

u - (u)^{- 1} = 2

Solve

u - u^{- 1} = 2 : u = 1 + 2, u = 1 - 2

u = 1 + 2, u = 1 - 2

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 1 + 2 : x = \frac{ln ( 1 + 2 )}{ln ( 5 )}

Solve

5^{x} = 1 - 2 :

No Solution for

x \in R

x = \frac{ln ( 1 + 2 )}{ln ( 5 )}

2^{3 x + 2} = 8

lo g_{7} (2^{4 + 3 x}) = 10

- 5 \cdot e^{10 t} = - 30

y, x^{y} = 3

e^{- x} = 4

What is the answer to 5^x-5^{-x}=2 ?
The answer to 5^x-5^{-x}=2 is x=(ln(1+sqrt(2)))/(ln(5))
Solve for x: 5^x-5^{-x}=2
The solution is x=(ln(1+sqrt(2)))/(ln(5))