What is the answer to 4^{x+1}+4^x=160 ?

The answer to 4^{x+1}+4^x=160 is x= 5/2

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4^{x+1}+4^x=160

4^{x + 1} + 4^{x} = 160

x = \frac{5}{2}

Decimal Notation

x = 2.5

Solution steps

4^{x + 1} + 4^{x} = 160

Factor

4^{x + 1} + 4^{x} : 5 \cdot 4^{x}

5 \cdot 4^{x} = 160

Divide both sides by

5

4^{x} = 32

Apply exponent rules

2 x = 5

Solve

2 x = 5 : x = \frac{5}{2}

x = \frac{5}{2}

5^{- x} = 3

3^{x} = 80

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

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

5^{2 x - 1} = 3^{x + 7}