/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 761 If \(\log _{4} 7=n\), find \(\lo... [FREE SOLUTION] | 91影视

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Chapter 26: Problem 761

If \(\log _{4} 7=n\), find \(\log _{4} 1 / 7\)

Short Answer

Expert verified
\(\log_{4} \frac{1}{7} = -n\)

Step by step solution

01

Recall the Rule of Logarithms

We need to use the rule of logarithms: \(\log_{a} \frac{1}{x} = -\log_{a} x\). This means that if the given expression is \(\log_{4} 7 = n\), we can find \(\log_{4} \frac{1}{7}\) by negating the given logarithm.
02

Apply the Rule

Apply the rule of logarithms to find \(\log_{4} \frac{1}{7}\): \[\log_{4} \frac{1}{7} = -\log_{4} 7\]
03

Use the Given Information

Now, we use the given information that \(\log_{4} 7 = n\). Replace the expression \(\log_{4} 7\) with the value of \(n\): \[\log_{4} \frac{1}{7} = -n\] Therefore, the value of \(\log_{4} \frac{1}{7}\) is \(-n\).

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