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Solve the equation $2^x + x = 5$

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Solve equations with variable exponents

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Q. Solve the equation

2^x + x = 5

Try Different Values: First, let's try some values for $x$ to see if we can find a pattern or a possible solution. $\newline$ Guess $x = 2$ . $\newline$ $2^2 + 2 = 4 + 2 = 6$ .
Testing $x = 2$ : $6$ is not equal to $5$ , so $x = 2$ is not the solution. $\newline$ Let's try $x = 1$ . $\newline$ $2^1 + 1 = 2 + 1 = 3$ .
Testing $x = 1$ : $3$ is also not equal to $5$ , so $x = 1$ is not the solution either. $\newline$ Let's try $x = 0$ . $\newline$ $2^0 + 0 = 1 + 0 = 1$ .
Testing $x = 0$ : $1$ is not equal to $5$ , so $x = 0$ is not the solution. $\newline$ Now, let's try $x = -1$ . $\newline$ $2^{-1} + (-1) = \frac{1}{2} - 1 = -\frac{1}{2}$ .
Testing $x = -1$ : $-\frac{1}{2}$ is not equal to $5$ , so $x = -1$ is not the solution. $\newline$ We need to try a different approach since guessing isn't working.
Trying $x = 3$ : Let's try $x = 3$ . $2^3 + 3 = 8 + 3 = 11$ .
Revisiting $x = 2$ : $11$ is not equal to $5$ , so $x = 3$ is not the solution. $\newline$ Let's go back and try $x = 2$ again. $\newline$ $2^2 + 2 = 4 + 2 = 6$ . $\newline$ Wait, we already tried $x = 2$ and it didn't work.

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