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Evaluate each expression. $\newline$ $\log_{7}343$

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Product property of logarithms

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Q. Evaluate each expression.

\newline

\log_{7}343

Recognize Relationship Base Logarithm: Recognize the relationship between the base of the logarithm and the argument. $\newline$ The argument of the logarithm is $343$ , and the base is $7$ . We need to determine the power to which the base $7$ must be raised to get $343$ .
Determine Power $343$ : Determine if $343$ is a power of $7$ . $\newline$ Since $7 \times 7 \times 7 = 343$ , we can see that $343$ is $7$ raised to the power of $3$ .
Apply Definition Logarithm: Apply the definition of a logarithm. $\newline$ By definition, $\log_{7} 343$ is the exponent to which $7$ must be raised to produce $343$ . From Step $2$ , we know this exponent is $3$ .
Write Final Answer: Write the final answer. $\newline$ Therefore, $\log_{7} 343$ is equal to $3$ .

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