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Math Help - change of base on logs

  1. #1
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    change of base on logs

    how does:

    log base 4 of 3

    become

    log base 2 of root 3?

    Im looking for the step by step please.
    Thanks in advance
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by 200001 View Post
    how does:

    log base 4 of 3

    become

    log base 2 of root 3?

    Im looking for the step by step please.
    Thanks in advance
    Change of base rule: \log_c{a} = \frac{\log_b{a}}{\log_b{c}}

    Power Rule: k\, \log_b{a} = \log_b{a^k}


    \log_4{3} = \frac{\log_2{3}}{\log_2{4}}



    Can you use those two rules to get the answer

    Spoiler:
    \log_2{4}  = 2

    \frac{1}{2} \log_2{3} = \log_2{3^{1/2}} = \log_2{\sqrt{3}}
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  3. #3
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    Joined
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    Yes, awesome, thanks
    i was missing my numerator on the half power and couldnt make the link between that and it becoming a power

    Much appreciated
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