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Math Help - Logorithms

  1. #1
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    Logorithms

    Hi! I'm afraid I really don't understand logorithms. If someone showed me how to answer the following questions I'd really help. Thanks!

    logy = 3x +2

    Find x when y = 500

    Find y when x = -1

    Express log(y^4) in terms of x

    Find an expression for y in terms of x


    And the logs are to base 10.
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  2. #2
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    Hello Tesphen
    Quote Originally Posted by Tesphen View Post
    Hi! I'm afraid I really don't understand logorithms. If someone showed me how to answer the following questions I'd really help. Thanks!

    logy = 3x +2

    Find x when y = 500
    Just put 500 into your calculator, press the log button, and solve for x:

    2.6990 = 3x + 2

    \Rightarrow  x = 0.2330


    Find y when x = -1
    When x=1, \log y = -3 + 2 = -1

    Now you need to use the definition of a logarithm, which is:

    • The log (to any base) of a number is that power to which the base must be raised in order to obtain the number.


    I know, confusing isn't it? So let's unpack it here. We have

     \log_{10} y = -1

    So -1 is the power to which the base (10) must be raised to obtain the number (that's y). So we have:

    y = 10^{-1} = 0.1

    It's really simple when you know how!

    Express log(y^4) in terms of x
    Here we use the law of logs: \log(a^b)=  b\log(a). So:

    \log(y^4) = 4\log(y) = 4(3x+2)

    And that's it!

    Find an expression for y in terms of x
    Again, we use the definition of a log that I've given you above. So here we have

    \log_{10}(y) = 3x + 2

    In other words, the log to base 10 of y is (3x+2). So, using the definition, (3x+2) is the power to which we must raise 10 to get y. So

    y = 10^{(3x+2)}

    And that's your expression for y in terms of x. I hope that helps to make it clearer!

    Grandad
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  3. #3
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    Thanks! That really helped.
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