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Math Help - Logarithmic Equation

  1. #1
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    Logarithmic Equation

    Solve the equation, log4 ^(m + 2) - log4^ (m - 5) = log4^ 8


    Is there a solution to this at all?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by BlueStar View Post
    Solve the equation, log4 ^(m + 2) - log4^ (m - 5) = log4^ 8


    Is there a solution to this at all?
    no there isn't

    i assume the 4 is not the base. in that case


    \log 4^{m + 2} - \log 4^{m - 5} = \log 4^8

    \Rightarrow \log \left( \frac {4^{m + 2}}{4^{m - 5}} \right) = \log 4^8

    \Rightarrow \log 4^7 = \log 4^8

    which is not true
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by BlueStar View Post
    Solve the equation, log4 ^(m + 2) - log4^ (m - 5) = log4^ 8


    Is there a solution to this at all?
    Here's another way to see that something is off with this equation

    \log 4^{m + 2} - \log 4^{m - 5} = \log 4^8

    \Rightarrow (m + 2) \log 4 - (m - 5) \log 4 = 8 \log 4

    \Rightarrow \left[ (m + 2) - (m - 5) \right] \log 4 = 8 \log 4

    equating coefficients we find

    \Rightarrow (m + 2) - (m - 5) = 8

    \Rightarrow 7 = 8 ---------> False
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  4. #4
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    Hello, BlueStar!

    I bet those 4's are bases . . .


    Solve the equation: . \log_4(m + 2) - \log_4(m - 5) \;= \;\log_4(8)

    We have: . \log_4\left(\frac{m+2}{m-5}\right) \;=\;\log_4(8)

    Then: . \frac{m+2}{m-5} \;=\;8\quad\Rightarrow\quad m + 2 \;=\;8m - 40\quad\Rightarrow\quad -7m \;=\;-42


    . . Therefore: . m \,=\,6

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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Soroban View Post
    Hello, BlueStar!

    I bet those 4's are bases . . .



    We have: . \log_4\left(\frac{m+2}{m-5}\right) \;=\;\log_4(8)

    Then: . \frac{m+2}{m-5} \;=\;8\quad\Rightarrow\quad m + 2 \;=\;8m - 40\quad\Rightarrow\quad -7m \;=\;-42


    . . Therefore: . m \,=\,6

    yes, i was thinking that as well. don't you just hate those typos?

    i made the statement that i assumed 4 was not the base, but BlueStar said nothing about it, unless he/she doesn't know what that means ...or it really wasn't the base, let's give BlueStar the benefit of the doubt
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