Problem

Simplify the following into a single logarithm: $4 \log (6)-4 \log (x)$

Answer

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Answer

So, the simplified form of the given expression is $\boxed{\log\left(\frac{6^4}{x^4}\right)}$

Steps

Step 1 ：Given the expression $4 \log (6)-4 \log (x)$

Step 2 ：Using the property of logarithms, $a \log (b) = \log (b^a)$, the expression can be rewritten as $\log (6^4) - \log (x^4)$

Step 3 ：Using another property of logarithms, $\log (a) - \log (b) = \log \left(\frac{a}{b}\right)$, the expression can be further simplified to $\log\left(\frac{6^4}{x^4}\right)$

Step 4 ：So, the simplified form of the given expression is $\boxed{\log\left(\frac{6^4}{x^4}\right)}$

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