What is the answer to 2^x+2^{x+3}=48 ?

The answer to 2^x+2^{x+3}=48 is x=(ln(16/3))/(ln(2))

Solve for x: 2^x+2^{x+3}=48

The solution is x=(ln(16/3))/(ln(2))

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2^{x} + 2^{x + 3} = 48

x = \frac{ln ( \frac{16}{3} )}{ln ( 2 )}

Decimal Notation

x = 2.41503 \dots

Solution steps

2^{x} + 2^{x + 3} = 48

Factor

2^{x} + 2^{x + 3} : 9 \cdot 2^{x}

9 \cdot 2^{x} = 48

Divide both sides by

9

2^{x} = \frac{16}{3}

Apply exponent rules

x ln (2) = ln (\frac{16}{3})

Solve

x ln (2) = ln (\frac{16}{3}) : x = \frac{ln ( \frac{16}{3} )}{ln ( 2 )}

x = \frac{ln ( \frac{16}{3} )}{ln ( 2 )}

e^{x} + 45 e^{- x} = 14

4 (\frac{1}{3})^{x} = 324

9^{3 x + 1} = 3

1 6^{x - 5} = 128

3^{x + 2} = 9^{x - 1}

What is the answer to 2^x+2^{x+3}=48 ?
The answer to 2^x+2^{x+3}=48 is x=(ln(16/3))/(ln(2))
Solve for x: 2^x+2^{x+3}=48
The solution is x=(ln(16/3))/(ln(2))