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Math Help - Logarithms questions

  1. #1
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    Logarithms questions

    Hi All,

    I have the following questions regarding logarithms:

    1) If a,b,c are distinct values, what is the value of abc if
    (logba)(logca) + (logab) (logcb)+ (logac) (logbc) -3 =0

    2) what is the value of x, if y = log7log7x and 5(y/log75) = 2


    Assume that logba means Loga to the base b
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, ayyappakumar!

    I hope I read #2 correctly.
    You should learn to use parentheses . . .


    2) Given: . {\color{blue}[1]}\;y \:=\: \log_7(\log_7x)\:\text{ and }\:{\color{blue}[2]}\;\frac{5y}{\log_75} \:=\: 2

    find the value of x.

    From [2], we have: . y \:=\:\tfrac{2}{5}\log_75\:=\:\log_7\!\left(5^{\fra  c{2}{5}}\right)

    Substitute into [1]: . \log_7(\log_7x) \:=\:\log_7\!\left(5^{\frac{2}{5}}\right)

    Exponentiate: . \log_7x \:=\:5^{\frac{2}{5}}

    \text{Exponentiate: }\;x \;=\;7^{\left(5^{\frac{2}{5}}\right)}

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