Question

what is the value of $\log_{7}343$?
-3
$\frac{1}{3}$
$\frac{1}{3}$
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 \(7\times7\times7 = 7^{3}=343\). So if \(7^{x}=7^{3}\), then by the property of exponents (if \(a^{m}=a^{n}\), then \(m = n\) for \(a>0,a
eq1\)), we get \(x = 3\).

Answer:

3 (corresponding to the option "3")