Problem
Solve the given equation. \[ 3^{-x}=0.863 \] \[ x= \] (Type an integer or a decimal. Round to three decimal places as needed.)
Solution
Step 1 ：The given equation is \(3^{-x} = 0.863\).
Step 2 ：This can be rewritten as \(x = \log_{0.863}(3)\).
Step 3 ：Using the logarithm properties, we can simplify this to \(x = -\log_{3}(0.863)\).
Step 4 ：Calculating the logarithm, we find that \(x \approx -0.134\).
Step 5 ：\(\boxed{x \approx -0.134}\)
