Solve for $x$
$27^{- x + 2} = 81$

Answer

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Answer

The solution to the equation is $\frac{2}{3}$ .

Steps

Step 1 ：Solve for $x$ in the equation $27^{- x + 2} = 81$ .

Step 2 ：Use the property of exponents that says $(a^{b})^{c} = a^{b c}$ to simplify the left side of the equation to $3^{3 (- x + 2)}$ .

Step 3 ：Set the simplified equation equal to $81$ , which is $3^{4}$ , to get $3^{3 (- x + 2)} = 3^{4}$ .

Step 4 ：Solve the equation for $x$ to get the solutions $x = \frac{2}{3}$ , $x = \frac{2}{3} - \frac{2 i π}{3 \log (3)}$ , and $x = \frac{2}{3} + \frac{2 i π}{3 \log (3)}$ .

Step 5 ：However, in the context of this problem, we are likely only interested in the real solution.

Step 6 ：The solution to the equation is $\frac{2}{3}$ .

Solve for x27−x+2=81

Answer

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Solve for $x$
$27^{- x + 2} = 81$