What is the answer to 81*9^{-2x-2}=27 ?

The answer to 81*9^{-2x-2}=27 is x=-3/4

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81*9^{-2x-2}=27

81 \cdot 9^{- 2 x - 2} = 27

x = - \frac{3}{4}

Decimal Notation

x = - 0.75

Solution steps

81 \cdot 9^{- 2 x - 2} = 27

Divide both sides by

81

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

Apply exponent rules

2 (- 2 x - 2) = - 1

Solve

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

x = - \frac{3}{4}

5 \cdot 1 0^{\frac{x}{4}} = 32

x + e^{x} = 0, x

9 = 3^{x + 1}

\frac{1}{5} = 5^{2 c + 3}

3^{x - 2} = 5^{2 x + 1}