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Math Help - REALLY really need an extra brain

  1. #1
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    REALLY really need an extra brain

    the last two problems of my homework for community college are tripping me up and I have been working on them ALL day my brain is on overload and it just won't crunch these numbers.. Help anyone>>??
    The directions are to solve by hand and show all work !
    problem #1) 2e^3x-1=54
    problem #2) 2log4(x^4)-3log4(3x)=3

    Both the 4's I made red because on my paper they are the bases .
    The e I made blue because it's the natural slanted e.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by cowgirl69 View Post
    the last two problems of my homework for community college are tripping me up and I have been working on them ALL day my brain is on overload and it just won't crunch these numbers.. Help anyone>>??
    The directions are to solve by hand and show all work !
    problem #1) 2e^3x-1=54
    problem #2) 2log4(x^4)-3log4(3x)=3

    Both the 4's I made red because on my paper they are the bases .
    The e I made blue because it's the natural slanted e.
    2e^{3x-1}=54

    e^{3x-1}=27

    3x-1=\ln(27)=\ln(3^3)=3\ln(3)

    3x=3\ln(3)+1

    x=\ln(3)+\frac{1}{3}
    ------------------------------------------------------------------------
    2\log_4(x^4)-3\log_4(3x)=3

    \log_4(x^8)-\log_4((3x)^3)=3

    \log_4\left(\frac{x^5}{27}\right)=3

    \frac{x^5}{27}=64

    x^{5}=1728

    x=\sqrt[5]{1728}
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