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Math Help - Log Equation

  1. #1
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    Log Equation

    Log(base6) - log(base 6)(x-1)=1

    MY SET UP:

    log_6[1/(x-1)] = 1

    6^1 = 1/(x-1)

    6 = 1/(x-1)

    6(x-1) = 1

    6x - 6 = 1

    6x = 7

    x = 7/6

    x = 1.2

    Right or wrong? If wrong, why?
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  2. #2
    o_O
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    Looks good to me
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  3. #3
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    That's correct.

    Quote Originally Posted by magentarita View Post
    Log(base6) - log(base 6)(x-1)=1

    MY SET UP:

    log_6[1/(x-1)] = 1

    6^1 = 1/(x-1)

    6 = 1/(x-1)

    6(x-1) = 1

    6x - 6 = 1

    6x = 7

    x = 7/6

    x = 1.2

    Right or wrong? If wrong, why?
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by magentarita View Post
    Log(base6) - log(base 6)(x-1)=1

    MY SET UP:

    log_6[1/(x-1)] = 1

    6^1 = 1/(x-1)

    6 = 1/(x-1)

    6(x-1) = 1

    6x - 6 = 1

    6x = 7

    x = 7/6

    x = 1.2

    Right or wrong? If wrong, why?
    It looks like you left something out of the question...

    \log_6\left(\dots\right)-\log_6\left(x-1\right)=1

    Would you fill in the dots?

    PS: If it is indeed \log_6\left(1\right)-\log_6\left(x-1\right)=1, then your work is correct.
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  5. #5
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    Quote Originally Posted by magentarita View Post
    Log(base6) - log(base 6)(x-1)=1

    MY SET UP:

    log_6[1/(x-1)] = 1

    6^1 = 1/(x-1)

    6 = 1/(x-1)

    6(x-1) = 1

    6x - 6 = 1

    6x = 7

    x = 7/6

    x = 1.2

    Right or wrong? If wrong, why?
    1. In the original equation the argument of the first log-term is missing. According to your calculations it seems to be 1.

    2. All calculations are correct - but \dfrac76 \neq 1.2

    3. You can control your work yourself by plugging in your solution into the original equation. If you get a true statement then your work is correct.

    ....

    121b) May I ask you a favour? Sometimes it is very difficult for me to read your questions. Why don't you use simply black colour for writing?
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  6. #6
    MHF Contributor
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    ok...

    I thank both replies. I will use simply black ink from now when asking questions.

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