Express as a single logarithm I am working on logarithms and have to express this as a single log:

Jeffery Clements

Jeffery Clements

Answered question

2022-06-14

Express as a single logarithm
I am working on logarithms and have to express this as a single log: 2 log a ( x ) 3 log a ( y )
I tried and came up with
2 log a ( x log a ( y ) )
but I'm not sure if I'm doing it right.

Answer & Explanation

Leland Ochoa

Leland Ochoa

Beginner2022-06-15Added 25 answers

You've got the right idea, but we need to consider the coefficients, as well. That is, before applying the fact that log x log y = log x y , we need to use the fact that
c log x = log x c
2 log a X 3 log a Y = log a X 2 log a Y 3 = log a ( X 2 Y 3 )

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