SOLUTION: Write these expressions as a single logarithm: 1. log3 24 + log3 2 2. 3 logx + 5 log y

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Question 585855: Write these expressions as a single logarithm:
1. log3 24 + log3 2

2. 3 logx + 5 log y
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Write these expressions as a single logarithm:
1. log3 24 + log3 2
Logs are the exponents. When you multiply terms, you add the exponents.
Adding logs --> multiplication
log3 24 + log3 2 = log%283%2C48%29
-----------------
2. 3 logx + 5 log y
3 times log(x) = log(x*x*x) multiplied
= log(x^3)
= log%28x%5E3%29+%2B+log%28y%5E5%29
= log%28x%5E3y%5E5%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +log%283%2C+24%29+%2B+log%283%2C+2%29+
Use the general rule:
+log%28a%29+%2B+log%28b%29+=+log%28a%2Ab%29+
(1) +log%283%2C48%29+
-------------------
(2) +3%2Alog%28x%29+%2B+5%2Alog%28y%29+
Use the previous rule and also:
+b%2Alog%28a%29+=+log%28a%5Eb%29+
(2) +log%28x%5E3%29+%2B+log%28y%5E5%29+
(2) +log%28%28+x%5E3y%5E5+%29%29+