Question

what is the value of \\(\log_{7} 343\\)?\
\\(\circ\\) \\(-3\\)\
\\(\circ\\) \\(-\frac{1}{3}\\)\
\\(\circ\\) \\(\frac{1}{3}\\)\
\\(\circ\\) \\(3\\)

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 \(7\times7\times7 = 7^{3}\), and \(7^{3}=343\). So from \(7^{x}=343\) and \(343 = 7^{3}\), we can conclude that \(x = 3\) because if \(7^{x}=7^{3}\), then \(x = 3\) (since the bases are the same and the exponential function is one - to - one).

Answer:

3 (corresponding to the option "3")