Does anyone know how to this problem? 4 * log3 + log2 writing it as a single logarithm

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Good idea to look up "Rules of Logarithms" and commit them to memory.  You'll need two such rules here.  One rule looks like this:

a log b = log b^a (a becomes the exponent of the argument b)

Apply this rule to the given 4 log 3.

The other rule has to do with products:  log a + log b = log a*b.

Apply this rule after you've followed my previous suggestion.