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Math Help - Some easy exercises i cannot wrap my head around...

  1. #1
    Newbie Crosswar's Avatar
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    Question Some easy exercises i cannot wrap my head around...

    So i have some exercises i simply just can not wrap my head around, they are not hard but for some reason i cannot understand them.
    Been doing some tests for school and it shows me the correct results in the end if i get it wrong.


    (x+4)/(9x+36) , the result is 1/9 if any1 can make me understand how it's made i would appreciate it.

    (6logx^2 + 6log1/x), i answered x^4/x^3 but the correct one is x^6, and i dont get it how.

    (e^8x)(e^5x)=68, this one i tried doing it with loge=68 and simplify the final result by 40 but it doesen't get me the correct answer.(0.3246)


    I realise this is preaty easy but i just need some help understanding it.

    Thank you.
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  2. #2
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    Awetuouncsygg
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    Re: Some easy exercises i cannot wrap my head around...

    1. Well, 9x+36=9\cdot x+9\cdot 4=9(x+4), so we can write our fraction this way:

    \frac{x+4}{9x+36}=\frac{x+4}{9(x+4)}=\frac{1}{9}


    2. You (should) know this: a\log x=\log x^a and this: \log x + \log y=\log xy. Now let's use the formulae for our exercise:

    6\log x^2 + 6\log \frac{1}{x}=\log (x^2)^6+\log \left (\frac{1}{x}  \right )^6=

    \log x^{12}+\log\frac{1}{x^6}=\log\left ( x^{12}\cdot  \frac{1}{x^6}\right )=\log \frac{x^{12}}{x^6}=\log x^6


    3. Uhm...

    e^{8x}\cdot e^{5x}=68 \Rightarrow e^{8x+5x}=68

    \Rightarrow e^{13x}=68  \Rightarrow \ln e^{13x}=\ln 68

    \Rightarrow 13x=\ln68 \Rightarrow x=\frac{\ln 68}{13}

    (ln 68)/13 - Wolfram|Alpha


    Hope I helped. ^^
    Thanks from Crosswar
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  3. #3
    Newbie Crosswar's Avatar
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    Re: Some easy exercises i cannot wrap my head around...

    Thank you so much, i spend like 40 min trying to figure it out.
    thank you.
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