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Math Help - Help with this sample proble for college entrance exam!!

  1. #1
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    Cool Help with this sample proble for college entrance exam!!

    Hi need help understanding how to simplify this expression with steps i do not know how these online math solvers got their answers.
    sqrt= square route ^means to the 1/3 power just in case you were confused.
    expression:

    4ln(sqrt(x))+6ln(x^(1/3))

    math solver got ln(x^4)

    any help will be appriciated thanks
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  2. #2
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    You need to make use of the formulas

    \displaystyle n\log{(x)} = \log{\left(x^n\right)} and \displaystyle \log{(a)} + \log{(b)} = \log{(ab)}.
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  3. #3
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    ok so how does that apply here i already got that the 6ln(x^(1/3))=2ln(x) right?? and i look for examples for a problem with the sqrt but cannot find any its been like 8 or 9 years sincer i was last using math like this. how would i simplify the 4ln(sqrt(x))???
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  4. #4
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    ohhhhhhhhhhhhhhhhhhh i think i got it so heres what i got for showing my work let me know

    4ln(sqrt(x))+6ln(x^(1/3))------------------>square the 4, and divide the 6 by 3 to isolate the x's
    2ln(x) + 2ln(x)
    4ln(x)----------------> using that rule n log(x) = log(x^n) thus getting the

    ln(x^4)
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  5. #5
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    You actually halve the 4, but yes, you have the general idea. Well done.
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