What is the answer to 81^{x/4}= 1/27 ?

The answer to 81^{x/4}= 1/27 is x=-3

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81^{x/4}= 1/27

8 1^{\frac{x}{4}} = \frac{1}{27}

x = - 3

Solution steps

8 1^{\frac{x}{4}} = \frac{1}{27}

Multiply both sides by

27

8 1^{\frac{x}{4}} \cdot 27 = \frac{1}{27} \cdot 27

Simplify

8 1^{\frac{x}{4}} \cdot 27 = 1

Divide both sides by

27

8 1^{\frac{x}{4}} = \frac{1}{27}

Apply exponent rules

x = - 3

3^{x + 1} (9^{2 - x}) = \frac{1}{3}

2^{x} - 3^{x} = 0

2^{2 x + 2} + 2^{x + 3} = 320

2^{x} + 2^{x + 3} = 72

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