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Math Help - logarithmic problem :|

  1. #1
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    logarithmic problem :|

    Given that , what is the value of ?




    Can anyone help me with this? Cheers x
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  2. #2
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    Quote Originally Posted by Haris View Post
    Given that , what is the value of ?

    Can anyone help me with this? Cheers x
    I assume that you mean:

    -2\cdot \log_b \left(5^{\frac12}\right)+5 \cdot \log_b \left(5^{4}\right) = 76 ............. If so:


    -2\cdot \frac12 \cdot \log_b (5)+5 \cdot 4 \cdot \log_b (5) = 76

    - \log_b (5)+20 \cdot \log_b (5) = 76

    \log_b(5)=\dfrac{76}{19}=4

    5 = b^4~\implies~\boxed{b=\sqrt[4]{5}}
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