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Math Help - One More Single Log

  1. #1
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    One More Single Log

    Write the expression below as a single logarithm.

    3 log_5 (3x + 1) - 2 log_5(2x - 1) - log_5 (x)

    NOTE: log_5 means "log base 5."
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  2. #2
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    Quote Originally Posted by magentarita View Post
    Write the expression below as a single logarithm.

    3 log_5 (3x + 1) - 2 log_5(2x - 1) - log_5 (x)

    NOTE: log_5 means "log base 5."
    = \log_5 (3x + 1)^3 - \log_5 (2x - 1)^2 - \log_5 (x)

    = \log_5 (3x + 1)^3 - \left[ \log_5 (2x - 1)^2 + \log_5 (x) \right]

    = \log_5 (3x + 1)^3 - \log_5 \left( (2x-1)^2 x \right)

    = \, ....
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  3. #3
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    Then...

    Is the last expression the answer?
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  4. #4
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    Quote Originally Posted by magentarita View Post
    Is the last expression the answer?
    Is the last expression in the form of a single logarithm?

    Now you have to use the log rule \log A - \log B = \log \frac{A}{B} to get an expression in the form of a single logarithm ....
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  5. #5
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    ok...

    That's what I thought.
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