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Math Help - write to single log

  1. #1
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    write to single log

    How do I start this? to make it one log?
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  2. #2
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    Log(a/b) = log(a) - log(b)
    log(ab) = log(a) + log(b)
    a log(b) = log(b^a)
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  3. #3
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    Quote Originally Posted by rj2001 View Post
    How do I start this? to make it one log?
    The start:

    12 \log_6 \sqrt{5x - 4} - \log_6 \left(\frac{6}{x} \right) + \log_6 6

     = 12 \log_6 (5x - 4)^{1/2} - \log_6 \left(\frac{6}{x} \right) + \log_6 6

     = \log_6 (5x - 4)^6 - \log_6 \left(\frac{6}{x} \right) + \log_6 6

    where the first term is got using one of the usual rules.

    Now add and subtract logs of the same base using the usual rules. Simplify.
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  4. #4
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    Hello, rj2001!

    Write as one log: . 12\log_6\sqrt{5x-4} - \log_6\left(\frac{6}{x}\right) + \log_6(6)

    \log_6\left(\sqrt{5x-4}\right)^{12} - \bigg[\log_6(6) - \log_6(x)\bigg] + \log_6(6)

    . = \;\log_6(5x-4)^6 - \log_6(6) + \log_6(x) + \log_6(6)

    . . = \;\log_6(5x-4)^6 + \log_6(x)

    . . = \;\log_6\bigg[x(5x-4)^6\bigg]

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