Problem Understanding: Understand the problem. We need to find the exponent to which the base 7 must be raised to get the number 343.Expressing 343 as a Power of 7: Express 343 as a power of 7. 343 is 7 raised to the power of 3, since 7 * 7 * 7 = 343.Applying the Definition of Logarithm: Apply the definition of logarithm. If log base 7 of 343 equals x, then 7^x = 343. Since we know that 343 is 7^3, we can say that x = 3.Concluding the Solution: Conclude the solution. Therefore, log base 7 of 343 is 3.

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$\log _{7} 343=$

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\log _{7} 343=

Problem Understanding: Understand the problem. $\newline$ We need to find the exponent to which the base $7$ must be raised to get the number $343$ .
Expressing $343$ as a Power of $7$ : Express $343$ as a power of $7$ . $\newline$ $343$ is $7$ raised to the power of $3$ , since $7 \times 7 \times 7 = 343$ .
Applying the Definition of Logarithm: Apply the definition of logarithm. $\newline$ If $\log_{7} 343 = x$ , then $7^{x} = 343$ . $\newline$ Since we know that $343$ is $7^{3}$ , we can say that $x = 3$ .
Concluding the Solution: Conclude the solution. $\newline$ Therefore, $\log_{7} 343 = 3$ .