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algebra2sucks
 3 years ago
Show why the log100 + log10000 = 2log(3)27
algebra2sucks
 3 years ago
Show why the log100 + log10000 = 2log(3)27

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satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0compute all the numbers and see that they are equal

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0you need \(\log(100)\) and also \(\log(10000)\) first

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0if you have a power of ten , the log counts the zeros

algebra2sucks
 3 years ago
Best ResponseYou've already chosen the best response.0lol i have no idea how to do this

ZeHanz
 3 years ago
Best ResponseYou've already chosen the best response.0When log 100 = a, this means: \[10^a=100\]Now, because 100 is a power of 10, you can see very quickly what log 100 is... Same for log 10000 >> what power of 10 is it?

ZeHanz
 3 years ago
Best ResponseYou've already chosen the best response.0If you have problems understanding logarithms, always remember one thing: LOGARITHMS are EXPONENTS

ZeHanz
 3 years ago
Best ResponseYou've already chosen the best response.0In your problem, I also see a logarithm with base 3. I will call it b: \[\log_{3} 27=b\]So b is that logarithm, base 3 of 27. This means, because logarithms are exponents, \[3^b=27\]Now, 27, doesn't it sound familiar? Yes! It is a power of 3! In fact, it is 3³:\[3^b=3^3\]so b = 3. The right hand side of the problem doubles that number, so we have 6 there. Can you see now, why the left hand side is 6 as well?

algebra2sucks
 3 years ago
Best ResponseYou've already chosen the best response.0Yea i guess so how do we answer this

ZeHanz
 3 years ago
Best ResponseYou've already chosen the best response.0Begin with the left hand side, replace log(100) and log(10000) with the numbers we've got. These will add up to 6. Right hand side is 2*3=6 also. Now you have shown that they are equal...

algebra2sucks
 3 years ago
Best ResponseYou've already chosen the best response.0so 6 is the answeR?

ZeHanz
 3 years ago
Best ResponseYou've already chosen the best response.0If you reread the question, you'll see that "6" ids not the answer. You have to show that the left hand side and right hand side are equal. Although they seem very different, both sides give you 6 if you calculate them. Therefore they are equal. That is what you had to prove.

algebra2sucks
 3 years ago
Best ResponseYou've already chosen the best response.0oh so how to i prove that with the equation right? i have no idea how to do this at all i know one side equals 6

algebra2sucks
 3 years ago
Best ResponseYou've already chosen the best response.0how do we get 6 for the left hand side?

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0\(\log(100)\) measn \(\log_{10}(100)\) and since \(100=10^2\) we know \(\log(100)=2\)

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0last job is to solve \(\log(10000)\) i.e. solve \(10^y=10000\) for \(y\)

algebra2sucks
 3 years ago
Best ResponseYou've already chosen the best response.03 would be the y?

ZeHanz
 3 years ago
Best ResponseYou've already chosen the best response.0What makes you think it is 3?

algebra2sucks
 3 years ago
Best ResponseYou've already chosen the best response.0because it has to equal to six idk i'm confused
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