document.write( "Question 360329: Express in a single logarithm using the product rule:
\n" ); document.write( " log 6 + log 6 = \n" ); document.write( "

Algebra.Com's Answer #257130 by jsmallt9(3758) $\"\"$ $\"About$

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The \"product rule\" is: $\"log%28a%2C+%28p%29%29+%2B+log%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Aq%29%29\"$ .
\n" ); document.write( "This allows us to combine the sum of any two logarithms of the same base and whose coefficients are 1's.

\n" ); document.write( "Using the \"product rule\" on
\n" ); document.write( "log(6) + log(6)
\n" ); document.write( "we get
\n" ); document.write( "log(6*6)
\n" ); document.write( "which simplifies to
\n" ); document.write( "log(36)

\n" ); document.write( "NOTE: We are not actually adding the logarithms with the \"product rule\". We are just combining them into a single, equivalent log using the pattern of the rule.
\n" ); document.write( "Your logarithms are of the same base and the arguments are the same so they are like terms and can be added. And one log(6) plus another log(6) gives us two log(6)'s:
\n" ); document.write( "log(6) + log(6) = 2log(6)
\n" ); document.write( "But this is not using the \"product rule\". \n" ); document.write( "

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