Question

question
what is the value of \\(\log_{7} \sqrt4{7}\\)?
answer attempt 1 out of 12

Explanation:

Step1: Rewrite the radical as an exponent

The fourth root of 7, \(\sqrt[4]{7}\), can be written as \(7^{\frac{1}{4}}\) using the property \(\sqrt[n]{a}=a^{\frac{1}{n}}\). So the expression becomes \(\log_{7}7^{\frac{1}{4}}\).

Step2: Apply the logarithm power rule

The power rule of logarithms states that \(\log_{a}b^{c}=c\log_{a}b\). Applying this rule, we get \(\frac{1}{4}\log_{7}7\).

Step3: Evaluate \(\log_{7}7\)

By the definition of a logarithm, \(\log_{a}a = 1\) for any positive \(a
eq1\). So \(\log_{7}7 = 1\). Then the expression becomes \(\frac{1}{4}\times1\).

Answer:

\(\frac{1}{4}\)