What is the answer to (5^x-5^{-x})/2 =3 ?

The answer to (5^x-5^{-x})/2 =3 is x=(ln(3+sqrt(10)))/(ln(5))

Solve for x: (5^x-5^{-x})/2 =3

The solution is x=(ln(3+sqrt(10)))/(ln(5))

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\frac{5 ^{x} - 5 ^{- x}}{2} = 3

x = \frac{ln ( 3 + 10 )}{ln ( 5 )}

Solution steps

\frac{5 ^{x} - 5 ^{- x}}{2} = 3

Multiply both sides by

2

\frac{5 ^{x} - 5 ^{- x}}{2} \cdot 2 = 3 \cdot 2

Simplify

5^{x} - 5^{- x} = 6

Apply exponent rules

5^{x} - (5^{x})^{- 1} = 6

Rewrite the equation with

5^{x} = u

u - (u)^{- 1} = 6

Solve

u - u^{- 1} = 6 : u = 3 + 10, u = 3 - 10

u = 3 + 10, u = 3 - 10

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 3 + 10 : x = \frac{ln ( 3 + 10 )}{ln ( 5 )}

Solve

5^{x} = 3 - 10 :

No Solution for

x \in R

x = \frac{ln ( 3 + 10 )}{ln ( 5 )}

2 (3^{x}) = 5

x = e^{x}

6^{1 - x} = 1 0^{x}

x^{l o g_{2} (x) + 2} = 8

What is the answer to (5^x-5^{-x})/2 =3 ?
The answer to (5^x-5^{-x})/2 =3 is x=(ln(3+sqrt(10)))/(ln(5))
Solve for x: (5^x-5^{-x})/2 =3
The solution is x=(ln(3+sqrt(10)))/(ln(5))