SOLUTION: Log5a+log5b-log5c

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Question 482777: Log5a+log5b-log5c
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%285%2Ca%29+%2B+log%285%2Cb%29+-+log%285%2Cc%29+
Make use of 2 rules
1st rule:
+log%28a%29+%2B+log%28b%29+=+log%28a%2Ab%29+
2nd rule:
+log%28a%29+-+log%28b%29+=+log%28a%2Fb%29+
------------------------
Using 1st rule:
+log%285%2Ca%29+%2B+log%285%2Cb%29+=+log%285%2Ca%2Ab%29+
Now I have:
+log%285%2Ca%2Ab%29+-+log%285%2Cc%29+
+log%285%2C+%28a%2Ab%29%2Fc%29+ answer
-------------------
Suppose
+a+=+5+
+b+=+25+
+c+=+625+
+log%285%2C5%29+%2B+log%285%2C25%29+=+1+%2B+2+
+1+%2B+2+=+3+
and
+3+-+log%285%2C625%29+=+3+-+3+=+0+
compare with:
+log%285%2C+%28a%2Ab%29%2Fc%29++=+log%285%2C+%285%2A25%29%2F635%29
which equals
+log%285%2C1%29+
The log to the base 5 which equals 1 is 0
OK