Question

solve: \log_{x}343 = 3\
x = \boxed{}\
done

Explanation:

Step1: Recall the logarithmic definition

The logarithmic equation \(\log_{x} 343 = 3\) can be converted to its exponential form using the definition \(\log_{a} b = c\) if and only if \(a^{c}=b\) (where \(a>0,a
eq1\)). So we have \(x^{3}=343\).

Step2: Solve for \(x\)

We need to find the value of \(x\) such that \(x^{3}=343\). We know that \(7\times7\times7 = 7^{3}=343\). So, taking the cube root of both sides of the equation \(x^{3}=343\), we get \(x=\sqrt[3]{343}=7\). Also, we need to check the domain of the logarithm. For \(\log_{x}343\) to be defined, \(x > 0\) and \(x
eq1\). Since \(7>0\) and \(7
eq1\), it is a valid solution.

Answer:

\(7\)