What is the answer to 2^{4x}(32^{1-x})=8^{x+2} ?

The answer to 2^{4x}(32^{1-x})=8^{x+2} is x=-1/4

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2^{4x}(32^{1-x})=8^{x+2}

2^{4 x} (3 2^{1 - x}) = 8^{x + 2}

x = - \frac{1}{4}

Decimal Notation

x = - 0.25

Solution steps

2^{4 x} (3 2^{1 - x}) = 8^{x + 2}

Apply exponent rules

4 x + 5 (1 - x) = 3 (x + 2)

Solve

4 x + 5 (1 - x) = 3 (x + 2) : x = - \frac{1}{4}

x = - \frac{1}{4}

5^{- x} = 25

2 7^{x - 1} = 9^{2 x}

5^{1 - 2 x} = 9

3^{x} = 500

4^{x} = 128

What is the answer to 2^{4x}(32^{1-x})=8^{x+2} ?
The answer to 2^{4x}(32^{1-x})=8^{x+2} is x=-1/4
Solve for x: 2^{4x}(32^{1-x})=8^{x+2}
The solution is x=-1/4