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Solve. Write your answer as an integer or a fraction in simplest form. $\newline$ $2^x = 16$ $\newline$ $x =$ ______

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Solve exponential equations by rewriting the base

Full solution

Q. Solve. Write your answer as an integer or a fraction in simplest form.

\newline

2^x = 16

\newline

x =

______

Express $16$ as Power of $2$ : Write $16$ as a power of $2$ . $16$ is $2$ raised to the power of $4$ , because $2 \times 2 \times 2 \times 2 = 16$ . So, $2^x = 2^4$ .
Solve for x: Solve for x. $\newline$ If $2^x = 2^4$ , then $x$ must equal $4$ because the bases are the same and therefore the exponents must be equal. $\newline$ $x = 4$ .

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