Write the expression as a sum and/or difference of logarithms. Express powers as factors.
\[
\log _{7}(2401 x)
\]
\[
\log _{7}(2401 x)=
\]
(Type an exact answer in simplified form.)

Answer

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Answer

So, the final answer is \(\boxed{4 + \log _{7}(x)}\)

Steps

Step 1 ：Given expression is \(\log _{7}(2401 x)\)

Step 2 ：Using the property of logarithms \(\log_b(mn) = \log_b(m) + \log_b(n)\), we can rewrite the expression as \(\log _{7}(2401) + \log _{7}(x)\)

Step 3 ：We know that \(7^4 = 2401\), so \(\log _{7}(2401) = 4\)

Step 4 ：Therefore, the simplified form of the given expression is \(4 + \log _{7}(x)\)

Step 5 ：So, the final answer is \(\boxed{4 + \log _{7}(x)}\)