Solve the equation $\displaystyle 27(9^{x+1}) = \frac{1}{81}$

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- Oct 11th 2010, 04:23 AMmastermin346indices problem
Solve the equation $\displaystyle 27(9^{x+1}) = \frac{1}{81}$

- Oct 11th 2010, 04:27 AMemakarov
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.