SOLUTION: condense each expression to a single logarithm {{{log(3,(a))+log(3,(b))+5*log(3,(c))}}} I am stuck on this question

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Question 224573: condense each expression to a single logarithm
log%283%2C%28a%29%29%2Blog%283%2C%28b%29%29%2B5%2Alog%283%2C%28c%29%29 I am stuck on this question
Found 2 solutions by drj, Edwin McCravy:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
condense each expression to a single logarithm

log3a+log3b+5log3c

The sum of the logarithms of each term is the log of their products.

Also 5log(3c)=log(3c)+log(3c)+log(3c)+log(3c)+log(3c)=log(3c*3c*3c*3c*3c)=log((3c)^5)



ANSWER: log%28%283a%29%29%2Blog%28%283b%29%29%2B5log%28%283c%29%29=log%28%282187abc%5E5%29%29

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

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Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
log%283%2C%28a%29%29%2Blog%283%2C%28b%29%29%2B5%2Alog%283%2C%28c%29%29

Use the rule of logs:  log%28n%2C%28X%29%29+%2B+log%28n%2C%28Y%29%29=+log%28n%2C%28XY%29%29
to rewrite the first two terms:

log%283%2C%28ab%29%29%2B5%2Alog%283%2C%28c%29%29 

Use the rule of logs:  log%28n%2C%28X%5EY%29%29=+Y%2Alog%28n%2C%28X%29%29
to rewrite the second term:


log%283%2C%28ab%29%29%2Blog%283%2C%28c%5E5%29%29

Use this rule of logs again:  log%28n%2C%28X%29%29+%2B+log%28n%2C%28Y%29%29=+log%28n%2C%28XY%29%29
to rewrite the expression:

log%283%2C%28abc%5E5%29%29

Edwin