Solve the equation $\displaystyle 27(9^{x+1}) = \frac{1}{81}$
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Step 1. Divide both sides by 27. Step 2. Express both sides as powers of 3. Note that $\displaystyle (3^2)^a=3^{2a}$ and $\displaystyle 3^{-a}=1/(3^a)$. Step 3. Equate the powers of 3 from the two sides.
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