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Math Help - Log help needed!

  1. #1
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    Log help needed!

    Hi there!

    Im a bit confused on the rules of logs, and im a bit stuck on this 2 part question.

    1. Write Log25 + Log21.6 as an integer.

    2. Solve the equation 2^x = 3

    And if you could sort of summarise or give a link with an explanation of logs it would be great.
    Thanks!
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  2. #2
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    Quote Originally Posted by nugiboy View Post
    Hi there!

    Im a bit confused on the rules of logs, and im a bit stuck on this 2 part question.

    1. Write Log25 + Log21.6 as an integer.

    2. Solve the equation 2^x = 3

    And if you could sort of summarise or give a link with an explanation of logs it would be great.
    Thanks!
    Someone correct me if I'm wrong, but for one, I believe, since they're both taking the log of 2, that you can simply add the two together, giving you the log 2 of 3.6.

    For two, take the log of 2 of both sides. It'll isolate x, and you should be able to solve it on a calculator.
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  3. #3
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    Hi thanks for the reply

    I checked in the answer, and its 3, which your method doesn't work out to be. Thanks for trying though. Your second answer worked.

    Can anyone else just verify?
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  4. #4
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    Ok, I got it on the first one.

    Use the change of base formula on both equations, and add them together.

    logx/loga
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  5. #5
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    Not quite sure about the change of base equation. Could someone explain to me in a bit more detail why and how it works etc. Sorry for being picky. Thanks though.
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  6. #6
    Senior Member DivideBy0's Avatar
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    Quote Originally Posted by nugiboy View Post
    Hi there!

    Im a bit confused on the rules of logs, and im a bit stuck on this 2 part question.

    1. Write Log25 + Log21.6 as an integer.

    2. Solve the equation 2^x = 3

    And if you could sort of summarise or give a link with an explanation of logs it would be great.
    Thanks!
    Hi nugiboy!

    Question 1

    \log_a x + \log_a y = \log_a {xy}

    Hence,

    log_2 5+\log_2 1.6 = \log_2 8 = 3

    Question 2

    If a^x = b, then \log_a b = x

    Hence,

    2^x = 3

    \Leftrightarrow x = \log_2 3

    If you want to evaluate on a calculator, use \frac{\log_a b}{\log_a c}=\log_c b

    \Rightarrow \log_2 3 = \frac{\log_{10} 3}{\log_{10} 2}\approx 1.58
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  7. #7
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    Quote Originally Posted by DivideBy0 View Post
    Hi nugiboy!

    Question 1

    \log_a x + \log_a y = \log_a {xy}

    Hence,

    log_2 5+\log_2 1.6 = \log_2 8 = 3

    Question 2

    If a^x = b, then \log_a b = x

    Hence,

    2^x = 3

    \Leftrightarrow x = \log_2 3

    If you want to evaluate on a calculator, use \frac{\log_a b}{\log_a c}=\log_c b

    \Rightarrow \log_2 3 = \frac{\log_{10} 3}{\log_{10} 2}\approx 1.58
    Hey thanks for that. I think i understand a bit better now. Do you know if there are any other necessary rules i should know about logs as im doing an As level math paper in a couple of weeks. What about dividing, taking away, and other equations?
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  8. #8
    Senior Member DivideBy0's Avatar
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    Here are the ones that I use:

    Note that we normally assume that a, b, c, and d are positive.

    1. \log_a b^n = n\log_a b

    2. \log_ab+\log_ac=\log_a{bc}

    3. \log_a b - \log_a c=\log_a{\left( \frac{b}{c}\right)}

    4. -\log_ab=\log_a{\left(\frac{1}{b}\right)} (derived from 3)

    5. (\log_ab)(\log_cd)=(\log_ad)(\log_cb)

    6. \frac{\log_ab}{\log_ac}=\log_cb

    7. \log_ab=\frac{1}{\log_ba}

    8. \log_{a^n} b^n=\log_a b

    You may only need the first four if you're studying basic logarithms, but the others are also incredibly useful.
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  9. #9
    Math Engineering Student
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    Quote Originally Posted by DivideBy0 View Post
    Note that we normally assume that a, b, c, and d are positive.
    Of course we require that logarithm base must be greater or equal than 2.

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  10. #10
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    Quote Originally Posted by DivideBy0 View Post
    Here are the ones that I use:

    Note that we normally assume that a, b, c, and d are positive.

    1. \log_a b^n = n\log_a b

    2. \log_ab+\log_ac=\log_a{bc}

    3. \log_a b - \log_a c=\log_a{\left( \frac{b}{c}\right)}

    4. -\log_ab=\log_a{\left(\frac{1}{b}\right)} (derived from 3)

    5. (\log_ab)(\log_cd)=(\log_ad)(\log_cb)

    6. \frac{\log_ab}{\log_ac}=\log_cb

    7. \log_ab=\frac{1}{\log_ba}

    8. \log_{a^n} b^n=\log_a b

    You may only need the first four if you're studying basic logarithms, but the others are also incredibly useful.
    Thanks very much. I think ive got everything i need there. I still need to work through them to make sure i understand them. Just wondering if any of the formulas you gave allow you to work with logs which don't have the same base.
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