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Math Help - Consider the equation.

  1. #1
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    Consider the equation.

    Consider the equation 10 = 2^x

    (a) Solve the equation for x by taking the common logarithm of both sides.

    Answer :
    log10 = xlog2
    x = log10/log2

    (b) use the result to show that 10 = 2^1/log2

    I understand that this works because log10 = 1, thus 1/log2 is the same thing as log10/log2. However, how does the power law of logarithm apply here? If i were to prove this question algebraically.

    (c) apply algebraic reasoning to show that 10 = 3^1/log10

    I get how this works in my mind, but i can't come up with an explanation, or the reasoning behind it.


    Thank you for the help,
    Jude
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  2. #2
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    Quote Originally Posted by purpledinosaur View Post
    Consider the equation 10 = 2^x

    (a) Solve the equation for x by taking the common logarithm of both sides.

    Answer :
    log10 = xlog2
    x = log10/log2

    (b) use the result to show that 10 = 2^1/log2

    I understand that this works because log10 = 1, thus 1/log2 is the same thing as log10/log2. However, how does the power law of logarithm apply here? If i were to prove this question algebraically.

    Simply substitute x = log10/log2 = 1/log2 into your original equation 10 = 2^x

    (c) apply algebraic reasoning to show that10 = 3^1/log10

    It doesn't.
    .
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  3. #3
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    Quote Originally Posted by purpledinosaur View Post
    Consider the equation 10 = 2^x

    (a) Solve the equation for x by taking the common logarithm of both sides.

    Answer :
    log10 = xlog2
    x = log10/log2

    (b) use the result to show that 10 = 2^1/log2

    I understand that this works because log10 = 1, thus 1/log2 is the same thing as log10/log2. However, how does the power law of logarithm apply here? If i were to prove this question algebraically.
    What you are saying is "algebraic". solving 10= 2^x to get x= 1/log(2) tells you exactly that 10= 2^(1/log(2))

    (c) apply algebraic reasoning to show that 10 = 3^1/log10
    You must mean that 10= 3^(1/log(3)), not log 10.
    And, of course, it is the same thing: taking the logarithm of both sides 10= 3^(1/log(3)) gives log(10)= 1= (1/log(3))(log(3))

    I get how this works in my mind, but i can't come up with an explanation, or the reasoning behind it.


    Thank you for the help,
    Jude
    Follow Math Help Forum on Facebook and Google+

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