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algebra2sucks

  • one year ago

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

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  1. satellite73
    • one year ago
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    compute all the numbers and see that they are equal

  2. satellite73
    • one year ago
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    you need \(\log(100)\) and also \(\log(10000)\) first

  3. satellite73
    • one year ago
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    if you have a power of ten , the log counts the zeros

  4. algebra2sucks
    • one year ago
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    lol i have no idea how to do this

  5. ZeHanz
    • one year ago
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    When 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?

  6. ZeHanz
    • one year ago
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    If you have problems understanding logarithms, always remember one thing: LOGARITHMS are EXPONENTS

  7. ZeHanz
    • one year ago
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    In 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?

  8. algebra2sucks
    • one year ago
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    Yea i guess so how do we answer this

  9. ZeHanz
    • one year ago
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    Begin 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...

  10. algebra2sucks
    • one year ago
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    so 6 is the answeR?

  11. ZeHanz
    • one year ago
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    If you re-read 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.

  12. algebra2sucks
    • one year ago
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    oh 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

  13. algebra2sucks
    • one year ago
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    how do we get 6 for the left hand side?

  14. satellite73
    • one year ago
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    \(\log(100)\) measn \(\log_{10}(100)\) and since \(100=10^2\) we know \(\log(100)=2\)

  15. satellite73
    • one year ago
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    last job is to solve \(\log(10000)\) i.e. solve \(10^y=10000\) for \(y\)

  16. algebra2sucks
    • one year ago
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    3 would be the y?

  17. algebra2sucks
    • one year ago
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    @satellite73 ?

  18. ZeHanz
    • one year ago
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    What makes you think it is 3?

  19. algebra2sucks
    • one year ago
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    because it has to equal to six idk i'm confused

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