What is the answer to 3^x-3^{-x}= 728/27 ?

The answer to 3^x-3^{-x}= 728/27 is x=3

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3^x-3^{-x}= 728/27

3^{x} - 3^{- x} = \frac{728}{27}

x = 3

Solution steps

3^{x} - 3^{- x} = \frac{728}{27}

Apply exponent rules

3^{x} - (3^{x})^{- 1} = \frac{728}{27}

Rewrite the equation with

3^{x} = u

u - (u)^{- 1} = \frac{728}{27}

Solve

u - u^{- 1} = \frac{728}{27} : u = 27, u = - \frac{1}{27}

u = 27, u = - \frac{1}{27}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 27 : x = 3

Solve

3^{x} = - \frac{1}{27} :

No Solution for

x \in R

x = 3

\frac{17}{327} = e^{- 9.22 \times 1 0^{- 4 t}}

7^{3 x + 4} = 4 9^{2 x + 1}

y, (3^{3})^{- 1} = x^{y}

e^{x + 9} = \frac{1}{e}

3^{x + 2} + 10 = 9^{x}

What is the answer to 3^x-3^{-x}= 728/27 ?
The answer to 3^x-3^{-x}= 728/27 is x=3
Solve for x: 3^x-3^{-x}= 728/27
The solution is x=3