What is the answer to 2^{3x}=16^{1-x} ?

The answer to 2^{3x}=16^{1-x} is x= 4/7

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2^{3x}=16^{1-x}

2^{3 x} = 1 6^{1 - x}

x = \frac{4}{7}

Decimal

x = 0.57142 \dots

Solution steps

2^{3 x} = 1 6^{1 - x}

Apply exponent rules

3 x = 4 (1 - x)

Solve

3 x = 4 (1 - x) : x = \frac{4}{7}

x = \frac{4}{7}

5 \cdot 1 0^{2 x} = 1

4^{2 x + 7} = 3 2^{2 x - 3}

(5^{x})^{- 1} = 25

32 = 2^{x - 3}

\frac{1}{16} = 2^{x}