I got these answers right on the practice SAT but can not figure out how to do them properly. Some of them I got right because I guess or just plugged them in. Any help would be wonderful.

1) If $\displaystyle (a+b)^{1/2}=(a-b)^{-1/2}$ which of the following must be true. The answer is $\displaystyle a^2-b^2=1$ But how? q.14-423

2) If $\displaystyle 2^{2x}=8^{x-1}$ what is the value of X? The answer is $\displaystyle 3$ but how, do you use log or something? q.9-397

3) The graph above shows Elina's height in inches from age 6 to 12. Elina's height at the age of 12 was what percent higher than her height at the age of 6? Her height at the age of 6 was 45 inches and her height at the age of 12 was 60 inches. The answer is $\displaystyle 33$ $\displaystyle 1/3$%. But how? q.15-399

All your help will be wholly and greatly appreciated.