Write the following as a single logarithm. Assume all variables are positive.
\[
3\left(\log _{2}(7)+\log _{2}(a)\right)-\log _{2}(7)=
\]

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Answer

So, the final answer is \(\boxed{\log _{2}\left(7^{2} a^{3}\right)}\)

Steps

Step 1 ：Given the expression \(3\left(\log _{2}(7)+\log _{2}(a)\right)-\log _{2}(7)\)

Step 2 ：Using the property of logarithms, we can rewrite the expression as \(\log _{2}(7^{3})+\log _{2}(a^{3})-\log _{2}(7)\)

Step 3 ：Then, we can combine the logs using the property \(\log_b(m) - \log_b(n) = \log_b(m/n)\), which gives us \(\log _{2}\left(\frac{7^{3}a^{3}}{7}\right)\)

Step 4 ：Simplify the expression inside the log to get \(\log _{2}\left(7^{2} a^{3}\right)\)

Step 5 ：So, the final answer is \(\boxed{\log _{2}\left(7^{2} a^{3}\right)}\)

Write the following as a single logarithm. Assume all variables are positive.\[3\left(\log _{2}(7)+\log _{2}(a)\right)-\log _{2}(7)=\]

Answer

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Write the following as a single logarithm. Assume all variables are positive.
\[
3\left(\log _{2}(7)+\log _{2}(a)\right)-\log _{2}(7)=
\]