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Solve. Write your answer as an integer or a fraction in simplest form. $\newline$ $49 = 7^x$ $\newline$ $x =$ ______

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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

49 = 7^x

\newline

x =

______

Rewrite as power of $7$ : Rewrite $49$ as a power of $7$ , since $7$ times $7$ is $49$ , we get $7^2$ . $\newline$ So, $49 = 7^2$ .
Set exponents equal: Now we have $7^x = 7^2$ . $\newline$ Since the bases are the same, we can set the exponents equal to each other. $\newline$ So, $x = 2$ .

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