anonymous
  • anonymous
2log6+log (1/3)=log12 which properties of logarithmics are/is used? power property and product property quotient property and product property quotient property only power property only
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Well If I asked you what 2log6 + log(1/3) was, how would you solve it (without using a calculator)?
anonymous
  • anonymous
my teacher didnt go over this but still put it on the end of course exam
anonymous
  • anonymous
log (1/3) is saying -log 3. With that we can use quotient property

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anonymous
  • anonymous
If it's just 2log6 +log(1/3) you can reduce it down to 2log6-log(3) because log(1) equal zero
anonymous
  • anonymous
2log6 can be written as log6^2 so, log 36
anonymous
  • anonymous
log36/log 3 is log 12
anonymous
  • anonymous
No it's not. log36 - log3 is log12.
anonymous
  • anonymous
same thing
anonymous
  • anonymous
make sense?
anonymous
  • anonymous
no it isn't. \[\frac{log\ 36}{log\ 3} \ne log(\frac{36}{3})\]
anonymous
  • anonymous
log36-log3 =log36/log3
anonymous
  • anonymous
i'm not saying log(36/3)
anonymous
  • anonymous
No, it doesn't. log 36 - log 3 = log(36/3)
anonymous
  • anonymous
>>> log(36, 10) - log(3, 10) 1.0791812460476247 >>> log(36,10)/log(3,10) 3.2618595071429146
anonymous
  • anonymous
Very different numbers.
anonymous
  • anonymous
try it in your calculator, (or wolframalpha)
anonymous
  • anonymous
log(36/3) is log(12) i checked with calculator and got the same answer so sorry for confusion just disregard the log36/log3
anonymous
  • anonymous
You can see quite trivially that it will be equal because 36/3 is 12. So log of 36/3 would be the log of 12. The problem is more about finding that log(36) - log(3) can be written as log(36/3)
anonymous
  • anonymous
ok so what was the problem?
anonymous
  • anonymous
The problem with your answer was that you said log(36) - log(3) = log(36)/log(3). But the simplest solution is to just say: \[2log6+log (1/3)\] \[=log36 + log(\frac{1}{3})\] \[=log (36 \times \frac{1}{3})\] \[=log(12)\] Which just uses the power and product rules. That said though you could also solve it by just using the product rule, or using the quotient rule and the power rule. So there's no non-ambiguous way to answer the multiple choice.

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