What is the answer to (1/2)^n=4^{n+1} ?

The answer to (1/2)^n=4^{n+1} is n=-2/3

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(1/2)^n=4^{n+1}

(\frac{1}{2})^{n} = 4^{n + 1}

n = - \frac{2}{3}

Decimal Notation

n = - 0.66666 \dots

Solution steps

(\frac{1}{2})^{n} = 4^{n + 1}

Apply exponent rules

- n = 2 (n + 1)

Solve

- n = 2 (n + 1) : n = - \frac{2}{3}

n = - \frac{2}{3}

2^{x} + 4^{x} = 1056

2 = (1 + \frac{0.06}{0.5})^{0.5 n}

26 = 220 (0.5)^{\frac{x}{6}}

e^{3 x} = 13.68

x, 4^{x + 5} - 4^{x + 4} = 384