To solve the equation [tex]\( 3^x = 2^{-x} + 4 \)[/tex], we need to determine the interval in which the solution lies by identifying two integers between which the solution exists.
Here's a step-by-step approach:
1. Define the equation: [tex]\( 3^x - 2^{-x} - 4 = 0 \)[/tex]
2. By examining the behavior of the function [tex]\( f(x) = 3^x - 2^{-x} - 4 \)[/tex], we can determine where the function changes sign, indicating a root between those points.
After analysis, we find that:
The solution to the equation [tex]\( 3^x = 2^{-x} + 4 \)[/tex] lies between the integer values of [tex]\( \boxed{1} \)[/tex] and [tex]\( \boxed{2} \)[/tex].
