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Solve for $x$ . $\newline$ $8 = 2^x$ $\newline$ $x =$ _____

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Understanding exponents

Full solution

Q. Solve for

x

.

\newline

8 = 2^x

\newline

x =

_____

Identify base and exponent: Identify the base and the exponent in the equation $8 = 2^x$ . $\newline$ In the equation, $2$ is the base and $x$ is the exponent. $\newline$ We need to find the value of $x$ such that $2$ raised to the power of $x$ equals $8$ .
Find powers of $2$ : Write down the powers of $2$ that are close to $8$ to find the correct exponent. $\newline$ $2^1 = 2$ $\newline$ $2^2 = 4$ $\newline$ $2^3 = 8$ $\newline$ We see that $2$ raised to the power of $3$ equals $8$ .
Compare with equation: Compare the result from Step $2$ with the equation $8 = 2^x$ . $\newline$ Since $2^3 = 8$ and our equation is $8 = 2^x$ , we can conclude that $x$ must be $3$ .

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