Hi. I just wanted to see if someone could check my work over. The only one im not so sure of is number 4 ( or bottom right) Thank you.
You were fine up to
$\displaystyle \ln \frac {a-b}{(a+b)^2} $
But then with the next step you have $\displaystyle (a+b)^2 = a^2+ b^2$, which is incorrect. If you multiply it out you get:
$\displaystyle (a+b)^2 = (a+b)(a+b) = a^2 + 2ab + b^2$.
In addition the step after that you go from $\displaystyle \frac {a+b}{a^2 + b^2}$ to $\displaystyle \frac {1 + b}{a + b^2}$. This too is incorrect - if you were trying to divide both numerator and denominator by 'a' you would get $\displaystyle \frac {1 + b/a}{a+ b^2/a}$.
Also, although you didn't ask - you have an error in the first one: check the sign of the $\displaystyle \log_a z^2$ term in the second line.
Ebaines - I actually meant for all of them to be checked so thank you for doing so. I think i have fixed the problem with number 4. Can you check again? I did it two different ways. I think they are both correct.
Thank you.