What is the answer to 2^x-2^{(x-2)}=3*2^{13} ?

The answer to 2^x-2^{(x-2)}=3*2^{13} is x=15

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2^x-2^{(x-2)}=3*2^{13}

2^{x} - 2^{(x - 2)} = 3 \cdot 2^{13}

x = 15

Solution steps

2^{x} - 2^{(x - 2)} = 3 \cdot 2^{13}

Factor

2^{x} - 2^{x - 2} : 3 \cdot 2^{x - 2}

3 \cdot 2^{x - 2} = 24576

Divide both sides by

3

2^{x - 2} = 8192

Apply exponent rules

x - 2 = 13

Solve

x - 2 = 13 : x = 15

x = 15

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

e^{2} = e^{2 x^{2} + 1}

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

e^{x - 1} = 12

34.1 \cdot 7.1 1^{x} = 120.28

What is the answer to 2^x-2^{(x-2)}=3*2^{13} ?
The answer to 2^x-2^{(x-2)}=3*2^{13} is x=15
Solve for x: 2^x-2^{(x-2)}=3*2^{13}
The solution is x=15