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Solve. Write your answer as an integer or a fraction in simplest form. $\newline$ $64 = 4^x$ $\newline$ $x =$ ______

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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

64 = 4^x

\newline

x =

______

Write as Power of $4$ : question_prompt: What is the value of $x$ when $64$ equals $4$ raised to the power of $x$ ? $\newline$ Step $1$ : Write $64$ as a power of $4$ . $\newline$ $64$ is the same as $4^3$ because $4 \times 4 \times 4$ equals $64$ . $\newline$ So, $64$ $0$
Set Equal to $4^3$ : Step $2$ : Set the equation $4^x$ equal to $4^3$ . $\newline$ Since $64 = 4^3$ , we have $4^x = 4^3$
Solve for x: Step $3$ : Solve for x. $\newline$ If $4^x = 4^3$ , then $x$ must equal $3$ because the bases are the same and therefore the exponents must be equal. $\newline$ $x = 3$

More problems from Solve exponential equations by rewriting the base

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\newline

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Posted 9 months ago

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Question

g(t) = 3^t

change over the interval from

t = 3

t = 4

\newline

\newline

g(t)

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g(t)

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g(t)

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g(t)

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Posted 4 months ago

Question

f(x)

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over every unit interval in

x

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\newline

Which could be a function rule for

f(x)

\newline

\newline

f(x) = 6x

\newline

f(x) = 6^x

\newline

f(x) = \frac{1}{6^x}

\newline

f(x) = \frac{x}{6}

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