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Solve. Write your answer as an integer or a fraction in simplest form. $\newline$ $256 = 4^x$ $\newline$ $x =$ ______

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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

256 = 4^x

\newline

x =

______

Recognize Power of $4$ : Recognize that $256$ is a power of $4$ . Calculate the powers of $4$ until reaching $256$ . $4^1 = 4$ , $4^2 = 16$ , $4^3 = 64$ , $4^4 = 256$ .
Calculate Powers of $4$ : Set the equation $4^x = 256$ equal to $4^4$ since $256$ equals $4^4$ .
Set Equation Equal: Since the bases are the same, set the exponents equal to each other. $x = 4$ .

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