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Rewrite as a quotient of two common logarithms. Write your answer in simplest form. $\newline$ $\log_5 7 =$ ______

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Change of base formula

Full solution

Q. Rewrite as a quotient of two common logarithms. Write your answer in simplest form.

\newline

\log_5 7 =

______

Identify Change of Base Formula: Identify the change of base formula for logarithms. The change of base formula allows us to rewrite a logarithm in terms of logarithms with a different base, typically base $10$ or base $e$ . The formula is: $\log_b(a) = \frac{\log_c(a)}{\log_c(b)}$ where $b$ is the original base, $a$ is the argument of the logarithm, and $c$ is the new base.
Apply Formula to $\log_5(7)$ : Apply the change of base formula to $\log_5(7)$ . We will use base $10$ for the common logarithms. According to the change of base formula: $\log_5(7) = \frac{\log(7)}{\log(5)}$
Check for Errors: Check for any mathematical errors. $\newline$ There are no mathematical errors in the application of the change of base formula.

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