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2log25 - 3log5 + log20 = ?
Guest Sep 28, 2014

Best Answer 

 #3
avatar+91412 
+10

Great work anon.    

I'm just going to look at it a slightly different way. 

$$\\2log25 - 3log5 + log20 \\
=2log5^2-3log5+log4+log5\\
=4log5-3log5+log2^2+log5\\
=2log5+2log2\\
=log25+log4\\
=log100\\
=log10^2\\
=2log10\\
=2*1\\
=2$$

 

You beat me Alan.   

Melody  Sep 28, 2014
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5+0 Answers

 #1
avatar
+8

2log25 - 3log5 + log20 =

2 log (5*5) -3 log 5 + log (2*2*5)

 

We know that: log (a*b)= log a + log b:

 

2 (log 5 + log 5) -3 log 5 + log 2 + log 2 + log 5=

4 log 5 - 3 log 5 +log 5 + 2 log 2=

2 log 5 + 2 log 2

Guest Sep 28, 2014
 #2
avatar+26397 
+10

You can take it just a little further Anonymous:

2log(5) + 2log(2) = log(52) + log(22) = log(25) + log(4) = log(25*4) = log(100) = 2 (assuming log to the base ten)

Alan  Sep 28, 2014
 #3
avatar+91412 
+10
Best Answer

Great work anon.    

I'm just going to look at it a slightly different way. 

$$\\2log25 - 3log5 + log20 \\
=2log5^2-3log5+log4+log5\\
=4log5-3log5+log2^2+log5\\
=2log5+2log2\\
=log25+log4\\
=log100\\
=log10^2\\
=2log10\\
=2*1\\
=2$$

 

You beat me Alan.   

Melody  Sep 28, 2014
 #4
avatar+80815 
+5

We have

2log25 - 3log5 + log20

2log(5*5) - 3log 5 + log (4*5)

2log 5 + 2log 5 - 3log 5 + log4 + log 5      combine like terms

5log5 - 3log 5 + log4 =

2log5 + log 4 =

log52 + log 4 =

log 25 + log 4 =

log (25*4) =

log 100 =

2

 

CPhill  Sep 28, 2014
 #5
avatar+80815 
+5

We have confirmed it ......the answer is   2 !!!!!!!

 

CPhill  Sep 28, 2014

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