what is the value of $\\log_{7}343$?\n-3\n$\\frac{1}{3}$\n$\\frac{1}{3}$\n3
what is the value of $\\log_{7}343$?\n-3\n$\\frac{1}{3}$\n$\\frac{1}{3}$\n3
Answer
Explanation:
Step1: Recall the definition of logarithm
The logarithm (\log_{a}b = x) is equivalent to (a^{x}=b). So for (\log_{7}343), we need to find (x) such that (7^{x}=343).
Step2: Express 343 as a power of 7
We know that (7\times7\times7 = 7^{3}=343). So if (7^{x}=7^{3}), then by the property of exponents (if (a^{m}=a^{n}), then (m = n) for (a>0,a\neq1)), we get (x = 3).
Answer:
3 (corresponding to the option "3")