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2^(x)=x+2

$2^{x}=x+2$

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Solve exponential equations by rewriting the base

Full solution

Q.

2^{x}=x+2

Identify Equation Type: Identify the type of equation. $\newline$ The equation $2^x = x + 2$ is a transcendental equation because it involves an exponential function and a polynomial function. There is no algebraic method to solve this type of equation directly. We will attempt to find a solution by inspection or simple substitution.
Check Obvious Solutions: Check for obvious solutions. $\newline$ We can check if small integer values of $x$ satisfy the equation. Let's start with $x = 0$ . $\newline$ $2^0 = 0 + 2$ $\newline$ $1 = 2$ $\newline$ This is not true, so $x = 0$ is not a solution.
Check $x = 1$ : Check the next integer value for $x$ . Let's try $x = 1$ . $2^1 = 1 + 2$ $2 = 3$ This is also not true, so $x = 1$ is not a solution.
Check $x = 2$ : Check the next integer value for $x$ . Let's try $x = 2$ . $2^2 = 2 + 2$ $4 = 4$ This is true, so $x = 2$ is a solution.

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