What is the answer to 3^x-1/(3^x)=10 ?

The answer to 3^x-1/(3^x)=10 is x=(ln(5+sqrt(26)))/(ln(3))

Solve for x: 3^x-1/(3^x)=10

The solution is x=(ln(5+sqrt(26)))/(ln(3))

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3^{x} - \frac{1}{3 ^{x}} = 10

x = \frac{ln ( 5 + 26 )}{ln ( 3 )}

Decimal Notation

x = 2.10487 \dots

Solution steps

3^{x} - \frac{1}{3 ^{x}} = 10

Apply exponent rules

3^{x} - (3^{x})^{- 1} = 10

Rewrite the equation with

3^{x} = u

u - (u)^{- 1} = 10

Solve

u - u^{- 1} = 10 : u = 5 + 26, u = 5 - 26

u = 5 + 26, u = 5 - 26

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 5 + 26 : x = \frac{ln ( 5 + 26 )}{ln ( 3 )}

Solve

3^{x} = 5 - 26 :

No Solution for

x \in R

x = \frac{ln ( 5 + 26 )}{ln ( 3 )}

Verify Solutions:

x = \frac{ln ( 5 + 26 )}{ln ( 3 )}

True

The solution is

x = \frac{ln ( 5 + 26 )}{ln ( 3 )}

e^{(2 x)} - 3 e^{(x)} - 10 = 0

2^{0.05 t} = 2

4 \cdot 3 2^{x} = \frac{1}{2}

7^{2 x} = 2 \cdot (5^{3 x + 1})

8^{x} = 2^{x + 6}

What is the answer to 3^x-1/(3^x)=10 ?
The answer to 3^x-1/(3^x)=10 is x=(ln(5+sqrt(26)))/(ln(3))
Solve for x: 3^x-1/(3^x)=10
The solution is x=(ln(5+sqrt(26)))/(ln(3))