Question

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

Explanation:

Step1: Recall the definition of a logarithm

The logarithm \(\log_{b}a = x\) is equivalent to \(b^{x}=a\). 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 \(7^{3}=343\).

Step3: Solve for \(x\)

Since \(7^{x}=343 = 7^{3}\), by the property of exponents (if \(b^{m}=b^{n}\), then \(m = n\) for \(b>0,b
eq1\)), we have \(x = 3\). So \(\log_{7}343=3\).

Answer:

3