What is the answer to 2^{2x+2}+2^{x+3}=320 ?

The answer to 2^{2x+2}+2^{x+3}=320 is x=3

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2^{2x+2}+2^{x+3}=320

2^{2 x + 2} + 2^{x + 3} = 320

x = 3

Solution steps

2^{2 x + 2} + 2^{x + 3} = 320

Apply exponent rules

(2^{x})^{2} \cdot 2^{2} + 2^{x} \cdot 2^{3} = 320

Rewrite the equation with

2^{x} = u

(u)^{2} \cdot 2^{2} + u \cdot 2^{3} = 320

Solve

u^{2} \cdot 2^{2} + u \cdot 2^{3} = 320 : u = 8, u = - 10

u = 8, u = - 10

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

2^{x} = - 10 :

No Solution for

x \in R

x = 3

2^{x} + 2^{x + 3} = 72

e^{2 x} = 3^{x - 4}

3 \cdot 3^{x} = 2 7^{2 x}

3 (2^{x - 3}) = 6^{x - 1}

9^{x - 10} = 1

What is the answer to 2^{2x+2}+2^{x+3}=320 ?
The answer to 2^{2x+2}+2^{x+3}=320 is x=3
Solve for x: 2^{2x+2}+2^{x+3}=320
The solution is x=3