What is the answer to 4^{x+2}-4^x=120 ?

The answer to 4^{x+2}-4^x=120 is x= 3/2

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4^{x+2}-4^x=120

4^{x + 2} - 4^{x} = 120

x = \frac{3}{2}

Decimal Notation

x = 1.5

Solution steps

4^{x + 2} - 4^{x} = 120

Factor

4^{x + 2} - 4^{x} : 15 \cdot 4^{x}

15 \cdot 4^{x} = 120

Divide both sides by

15

4^{x} = 8

Apply exponent rules

2 x = 3

Solve

2 x = 3 : x = \frac{3}{2}

x = \frac{3}{2}

15 - e^{x - 8} = 4

x^{x^{49}} = 7^{7^{5}}

e^{- x} + e^{- 2 x} = \frac{2}{3}

4^{x} - 12 \times 2^{x} + 32 = 0