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Math Help - logarithms questions

  1. #1
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    logarithms questions

    could somebody help me with these questions...being able to see the work would be awesome and incredibly helpful! thank you!

    1) write as a single logarithm and solve :
    2log3(12)-2log3(4)

    2)write as a single logarithm:
    log3(x+2)-logx(2x-1)+log3(5)

    3)solve for x: logx(x-1)=log8(x-1)
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  2. #2
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    Hello,

    You should know some formulae for logarithms. Then, 1) and 2) are easy.

    For 3), you see that x-1>0 (in order for the log to be defined.)
    Then, the equation becomes \frac{\log_8(x-1)}{\log_8x}=\log_8(x-1).

    Bye.
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  3. #3
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    HEY,

    3) Since the question is asking u to solve to find x
    then x has a value
    just looking at the eqation you can conclude that
    (x=8), since its similar and there is an = sign
    soooo the bases have to be the same too.

    For 1 and 2, dude its veryyyyy simple
    you just need to know 4 basic rules.

    1) nLog x = Log x^n
    2) Log(base-C)A + Log(base-C)B = Log(baseC)A*B
    3) Log(base-C)A - Log(base-C)B = Log(baseC)A/B
    4) Log (base-x)x^n = n Log (base-x)x =n

    * = times

    Back to ur questions

    1) 2log3(12) - 2log3(4)
    if i am correct 3 is the base????

    Log (base3) 12^2 - Log (base3) 4^2
    Log (base3) 144 - Log (base3) 16
    Log (base3) 144/16
    Log (base3) 9 (thats the single logarithm)

    We can further simplify it to solve it
    Log (base3) 3^2
    2 Log (base3) 3
    = 2

    2) Log 3(x+2) - Log x(2x-1) + log 3(5)
    = Log (3x+6) - log (2x^2 -x) + log 15

    = log (3x+6)/(2x^2 -x) * 15
    = log (45x+90)/(2x^2 -x)

    I hope this helpes
    cheers
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  4. #4
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    Quote Originally Posted by whatsgoingon View Post
    could somebody help me with these questions...being able to see the work would be awesome and incredibly helpful! thank you!

    1) write as a single logarithm and solve :
    2log3(12)-2log3(4)

    2)write as a single logarithm:
    log3(x+2)-logx(2x-1)+log3(5)

    3)solve for x: logx(x-1)=log8(x-1)
    Here are the general rules. Using these should enable you to solve your question. You may need to use more than one rules for some of your questions.

    a\log_x(y)=\log_x(y^a)

    \log_x(y) + \log_x(z) = \log_x(yz)

    \log_x(y) - \log_x(z) = \log_x\left(\frac{y}{z}\right)

    \log_x(y) = \frac{\log_z(y)}{\log_z(x)}

    a^y = x \rightarrow y=\log_a(x)
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