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marcelie

  • one year ago

Help please how do i solve this log equation. Please show me the steps . log 9 (1/729)

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  1. marcelie
    • one year ago
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    |dw:1443995786278:dw|

  2. Jhannybean
    • one year ago
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    Change of base formula : \(\log_b(x) = \dfrac{\log_d (x)}{\log_d (b)}\)

  3. marcelie
    • one year ago
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    ah okay. is that the same thing as log b(m/n ) = log b M - log b N ?

  4. Jhannybean
    • one year ago
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    No.

  5. Jhannybean
    • one year ago
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    Just treat \(\frac{1}{729}\) as \(x\) :)

  6. marcelie
    • one year ago
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    oh okay . Got it :) ty

  7. Jhannybean
    • one year ago
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    So what did you get as your answer?

  8. marcelie
    • one year ago
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    i got -3

  9. Jhannybean
    • one year ago
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    Awesome!! good job.

  10. Jhannybean
    • one year ago
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    This is how I did it

  11. marcelie
    • one year ago
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    :)

  12. Jhannybean
    • one year ago
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    \[729 = 3^6, \qquad 9 = 3^2 \]\[\begin{align} \log_9 \left(\frac{1}{729}\right) &= \frac{\log\frac{1}{729}}{\log(9)} \\\ &= \frac{\log(1)-\log(729)}{\log(9)} \\\ & = \frac{-\log(3^6)}{\log(3^2)} \\\ &= -\frac{6\log(3)}{2\log(3)} \\\ &= -3\end{align} \]

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spraguer (Moderator)
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