Solve the given equation.
\[
3^{-x}=0.863
\]
\[
x=
\]
(Type an integer or a decimal. Round to three decimal places as needed.)

Answer

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Answer

\(\boxed{x \approx -0.134}\)

Steps

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 ：\(\boxed{x \approx -0.134}\)