1. ## 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.

2. ## 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. ^^

3. ## 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.