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

The answer to 2^{x+2}+2^x=2^2 is x=(ln(4/5))/(ln(2))

Solve for x: 2^{x+2}+2^x=2^2

The solution is x=(ln(4/5))/(ln(2))

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2^{x + 2} + 2^{x} = 2^{2}

x = \frac{ln ( \frac{4}{5} )}{ln ( 2 )}

Decimal Notation

x = - 0.32192 \dots

Solution steps

2^{x + 2} + 2^{x} = 2^{2}

Factor

2^{x + 2} + 2^{x} : 5 \cdot 2^{x}

5 \cdot 2^{x} = 4

Divide both sides by

5

2^{x} = \frac{4}{5}

Apply exponent rules

x ln (2) = ln (\frac{4}{5})

Solve

x ln (2) = ln (\frac{4}{5}) : x = \frac{ln ( \frac{4}{5} )}{ln ( 2 )}

x = \frac{ln ( \frac{4}{5} )}{ln ( 2 )}

3^{a} = - 1

3^{y} + 3^{y} + 2 = \frac{10}{3}

x, 2^{x + 1} \cdot 3^{y - 1} = (2 \cdot 3)^{5}

\frac{( \frac{( 2 ^{x} )}{16} ) ^{x} - 1}{16} = 0

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

What is the answer to 2^{x+2}+2^x=2^2 ?
The answer to 2^{x+2}+2^x=2^2 is x=(ln(4/5))/(ln(2))
Solve for x: 2^{x+2}+2^x=2^2
The solution is x=(ln(4/5))/(ln(2))