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Math Help - Simple Logarithm

  1. #1
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    Simple Logarithm

    I have a problem solving a very simple logarithm problem.

    \log_8 128 = ?

    I know that the answer is 7/3 but i don't know how the answer is derived. Can someone explain all the step .

    Thanks.
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  2. #2
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    Quote Originally Posted by vivek_master146 View Post
    I have a problem solving a very simple logarithm problem.

    \log_8 128 = ?

    I know that the answer is 7/3 but i don't know how the answer is derived. Can someone explain all the step .

    Thanks.
    128=2^7

    8=2^3

    and:

    \log_8(128)=\dfrac{\log_2(128)}{\log_2(8)}
    CB
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  3. #3
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    Quote Originally Posted by vivek_master146 View Post
    I have a problem solving a very simple logarithm problem.

    \log_8 128 = ?

    I know that the answer is 7/3 but i don't know how the answer is derived. Can someone explain all the step .

    Thanks.
    \displaystyle \frac{7}{3} is correct, because

    \displaystyle \log_8{128} = \log_8{(8^{\frac{7}{3}})} = \frac{7}{3}\log_8{8} = \frac{7}{3}.
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  4. #4
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    You can also change to exponential form first and get a common base:

    \log_8 128 = x

    8^x=128

    (2^3)^x=2^7

    2^{3x}=2^7

    3x=7

    x=\frac{7}{3}
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