title: Log and exponent conversion in Big Oh notation
body: <p>I'm doing some basic Big-oh problems in class and when reading the answer key, I'm having trouble understanding these log conversions that my professor did. I'd appreciate it if someone could write out the steps.</p>
  <ol>
  <li>We are trying to show that <img src="https://latex.codecogs.com/gif.latex?n%5E%7B%5Csqrt(n)%7D&amp;space;%5Cneq&amp;space;%5CTheta&amp;space;(2%5En)" alt="formula" /> and this is the first step <img src="https://latex.codecogs.com/gif.latex?n%5E%7B%5Csqrt(n)%7D&amp;space;=&amp;space;2%5E%7B%5Csqrt(n)%5Clog&amp;space;n%7D" alt="formula" />
  which i dont understand</li>
  <li>we are showing that <img src="https://latex.codecogs.com/gif.latex?%5Clog_%7B%5Csqrt(n)%7Dn&amp;space;%5Cneq&amp;space;%5Ctheta(%5Clog_2%5Csqrt(n))" alt="formula" /> and the first step is <img src="https://latex.codecogs.com/gif.latex?%5Clog_%7B%5Csqrt(n)%7Dn&amp;space;=&amp;space;1/2" alt="formula" /></li>
  <li>We are showing <img src="https://latex.codecogs.com/gif.latex?%5Clog(n)%5E%7B%5Clog(n)%7D%5Cneq&amp;space;%5Ctheta(n%5E%7B100%7D)" alt="formula" /> and the first step is <img src="https://latex.codecogs.com/gif.latex?%5Clog(n)%5E%7B%5Clog(n)%7D&amp;space;=&amp;space;n%5E%7B%5Clog&amp;space;%5Clog(n)%7D" alt="formula" /></li>
  </ol>
  <p>Thank you!</p>