What is the answer to 2^{-(x+3)}=32^x ?

The answer to 2^{-(x+3)}=32^x is x=-1/2

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2^{-(x+3)}=32^x

2^{- (x + 3)} = 3 2^{x}

x = - \frac{1}{2}

Decimal Notation

x = - 0.5

Solution steps

2^{- (x + 3)} = 3 2^{x}

Apply exponent rules

- (x + 3) = 5 x

Solve

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

x = - \frac{1}{2}

(5^{x})^{3} = 25 \cdot 12 5^{x}

5^{b} \cdot 5^{b} = 5^{2 b}

0.5 \cdot e^{4 x} = 13

8 1^{2 x - 2} - 2 7^{4 - 5 x} = 0

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