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Math Help - Logs

  1. #1
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    Logs

    Determine value of the expression 1/logbase9(15) + 1/logbase25(15)
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  2. #2
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    First add the fractions, then use the change of base formula log_bx=\frac{log_ax}{log_ab}
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  3. #3
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    Quote Originally Posted by Tiger View Post
    Determine value of the expression 1/logbase9(15) + 1/logbase25(15)
    Use the change of base rule: log_c(a) = \frac{log_b(a)}{log_b(c)}

    log_{9}(15) = \frac{ln(15)}{ln(9)}

    log_{25}(15) = \frac{ln(15)}{ln(25)}

    Flipping the two results above and adding gives: \frac{ln(25)+ln(9)}{ln(15)}

    Simplify using the log multiplication rule: a\,ln(k) = ln(k^a)

    \frac{ln(25)+ln(9)}{ln(15)} = \frac{2[ln(5)+ln(3)]}{ln(15)}


    Simplify using the log addition rules: ln(a)+ln(b) = ln(ab)<br />

    \frac{2[ln(5)+ln(3)]}{ln(15)} = \frac{2ln(15)}{ln(15)} = 2
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