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    Find a if Log2a – log8a = 2
    I have spent hours trying to answer it but still really stuck ?
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    Even if just to put me on the right lines, if the base was a letter, I would know how to use the division rule, but this is one is different
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    I half remembered a similar question but couldn't quite so I looked it up. This might help.


    Change of base formula. Logb x = Loga x/Loga b. Pick a new base and the formula says it is equal to the log of the number in the new basedivided by the log of the old base in the new base.

    You could change log8a to a fraction in log 2. I think that works out then.
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    (Original post by maggiehodgson)
    I half remembered a similar question but couldn't quite so I looked it up. This might help.


    Change of base formula. Logb x = Loga x/Loga b. Pick a new base and the formula says it is equal to the log of the number in the new basedivided by the log of the old base in the new base.

    You could change log8a to a fraction in log 2. I think that works out then.
    so do you mean that Logb2 = loga8 - loga2?
    really stuck sorry
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    (Original post by Sam00)
    so do you mean that Logb2 = loga8 - loga2?
    really stuck sorry
    log8a can be turned into log2a/log28 if I've read the instructions properly. Log28 = 3
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    (Original post by maggiehodgson)
    log8a can be turned into log2a/log28 if I've read the instructions properly. Log28 = 3
    where did you get the 28 from?
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    (Original post by Sam00)
    Find a if Log2a – log8a = 2
    I have spent hours trying to answer it but still really stuck ?
    I'm glad you asked because I still haven't found a way around it haha! I did see the rule mentioned above yesterday but I can't see how to apply it to this question.
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    The 2 is a subscript (can't use latex)

    I'm writing out the solution and I'll attach it if you can't get any further now that you know all my 2s are subscripts
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    (Original post by Sam00)
    where did you get the 28 from?
    I think they meant log(base 2)8
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    The answer is a=8
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    (Original post by Sam00)
    Find a if Log2a – log8a = 2
    I have spent hours trying to answer it but still really stuck ?
    Have you managed it yet?
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    (Original post by Sam00)
    Find a if Log2a – log8a = 2
    I have spent hours trying to answer it but still really stuck ?
    \log_8 a = \frac{\log_2 a}{\log_2 8} = \frac{\log_2 a}{\log_2 2^3} = \frac{\log_2 a}{3 \log_2 2} = \frac{\log_2 a}{3}

    So \log_2 a - \log_8 a = 2 \iff \log_2 a - \frac{\log_2 a}{3} = \log_2 4 \iff \frac{2}{3} \log_2 a = \log_2 4

    Then  \log_2 a^{2/3} = \log_2 4 \Rightarrow a^{2/3} = 4.

    Are you going to delete and mutilate this thread as you have to all your other threads?
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    (Original post by Qcomber)
    The answer is a=8
    How enlightening.
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    You can think about it intuitively or use the formal change of base rule as follows  \displaystyle \log_ab=\frac{\log_cb}{\log_ca} where c is any number you like.

    In this case  \displaystyle log_2a=\frac{\log_8a}{\log_82} \Rightarrow \log_2a = 3\log_8a which makes sense if you think about it.
    Plug this result into the equation and it should be straight forward from there.
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    (Original post by Sam00)
    Find a if Log2a – log8a = 2
    I have spent hours trying to answer it but still really stuck ?
    Here is a link to the proof of the question you asked.

    https://www.khanacademy.org/math/alg...-formula-proof
 
 
 
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