What is the answer to 2^{x+2}+5\times 2^{x-1}= 13/16 ?

The answer to 2^{x+2}+5\times 2^{x-1}= 13/16 is x=-3

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2^{x+2}+5\times 2^{x-1}= 13/16

2^{x + 2} + 5 \cdot 2^{x - 1} = \frac{13}{16}

x = - 3

Solution steps

2^{x + 2} + 5 \cdot 2^{x - 1} = \frac{13}{16}

Factor

2^{x + 2} + 5 \cdot 2^{x - 1} : 13 \cdot 2^{x - 1}

13 \cdot 2^{x - 1} = \frac{13}{16}

Divide both sides by

13

2^{x - 1} = \frac{1}{16}

Apply exponent rules

x - 1 = - 4

Solve

x - 1 = - 4 : x = - 3

x = - 3

4 e^{3 - x} = 3^{2 x + 5}

5^{n} = 125

- e^{- x} - 1 = 0

e^{- 2 x} = \frac{1}{2}

2^{x - 3} = 1

What is the answer to 2^{x+2}+5\times 2^{x-1}= 13/16 ?
The answer to 2^{x+2}+5\times 2^{x-1}= 13/16 is x=-3
Solve for x: 2^{x+2}+5\times 2^{x-1}= 13/16
The solution is x=-3