Question

question
what is the value of \\(\log_{7} \sqrt4{343}\\)?

answer attempt 1 out of 2

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Explanation:

Step1: Simplify the radical

First, we know that \(343 = 7^3\), so \(\sqrt[4]{343}=\sqrt[4]{7^3}\). By the property of radicals \(\sqrt[n]{a^m}=a^{\frac{m}{n}}\), we can rewrite this as \(7^{\frac{3}{4}}\).

Step2: Apply the logarithm property

Now we have \(\log_{7}7^{\frac{3}{4}}\). Recall the logarithm property \(\log_{a}a^x = x\) (where \(a>0,a
eq1\)). Here, \(a = 7\) and \(x=\frac{3}{4}\), so \(\log_{7}7^{\frac{3}{4}}=\frac{3}{4}\).

Answer:

\(\frac{3}{4}\)