What is the answer to 2^{2+x}-2^{2-x}=15 ?

The answer to 2^{2+x}-2^{2-x}=15 is x=2

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2^{2+x}-2^{2-x}=15

2^{2 + x} - 2^{2 - x} = 15

x = 2

Solution steps

2^{2 + x} - 2^{2 - x} = 15

Apply exponent rules

2^{x} \cdot 2^{2} - (2^{x})^{- 1} \cdot 2^{2} = 15

Rewrite the equation with

2^{x} = u

u \cdot 2^{2} - (u)^{- 1} \cdot 2^{2} = 15

Solve

u \cdot 2^{2} - u^{- 1} \cdot 2^{2} = 15 : u = 4, u = - \frac{1}{4}

u = 4, u = - \frac{1}{4}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 4 : x = 2

Solve

2^{x} = - \frac{1}{4} :

No Solution for

x \in R

x = 2

2^{3 - 2 x} = 8

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

9^{x - 5} = 1 2^{x}

4^{x} + 4^{x + 1} = 20 \cdot 4

What is the answer to 2^{2+x}-2^{2-x}=15 ?
The answer to 2^{2+x}-2^{2-x}=15 is x=2
Solve for x: 2^{2+x}-2^{2-x}=15
The solution is x=2