Converting sum of logarithms to the logarithm of a product?

Questions
,
1

I know there is some sort of external function to convert

Log[x]+Log[y]

into

Log[x y]

but cannot find it. Any help?

2

Greetings Bob, from Sy Blinder

The rule for sum of logs doesn’t appear to be built in to Mathematica. But try the following workaround:

In[13]:= Log[Exp[Log[x] + Log[y]]]

Out[13]= Log[x y]
3

You can do it with Simplify with assumptions

Simplify[Log[x] + Log[y], x > 0 && y > 0]

or with a replacement rule:

logRule = a_. Log[x_] + b_. Log[y_] :> Log[x^a*y^b];
Log[x] + Log[y] - Log[3] //. logRule

Beware that the rule has restrictions on its valididy.

4

Thanks for the help. Both ideas look good. Bob