Evaluate each expression. log_(7)343

Recognize Relationship Base Logarithm: Recognize the relationship between the base of the logarithm and the argument. 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. Since 7 * 7 * 7 = 343, we can see that 343 is 7 raised to the power of 3.Apply Definition Logarithm: Apply the definition of a logarithm. By definition, log base 7 of 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. Therefore, log base 7 of 343 is equal to 3.

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

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Precalculus

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 $3$ .