What is the answer to (1/4)^x=8^{x+1} ?

The answer to (1/4)^x=8^{x+1} is x=-3/5

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(1/4)^x=8^{x+1}

(\frac{1}{4})^{x} = 8^{x + 1}

x = - \frac{3}{5}

Decimal Notation

x = - 0.6

Solution steps

(\frac{1}{4})^{x} = 8^{x + 1}

Apply exponent rules

- 2 x = 3 (x + 1)

Solve

- 2 x = 3 (x + 1) : x = - \frac{3}{5}

x = - \frac{3}{5}

5 e^{2 x} = 3

5^{x + 1} + 5^{x} = 750

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

2 5^{x} = 5^{x^{2} - 3}

(\frac{1}{2})^{x - 1} = 8