# User:Lilylee

 This works: $\begin{matrix} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{matrix}$ $\begin{matrix} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\  \end{matrix}$ This doesn't work: \begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align} \begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\  \end{align}
 This works: $\begin{matrix} z & = & a \\ f(x,y,z) & = & x + y + z \end{matrix}$ $\begin{matrix}  z & = & a \\ f(x,y,z) & = & x + y + z  \end{matrix}$ This doesn't work: $\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}$ $\begin{array}{lcl}  z & = & a \\ f(x,y,z) & = & x + y + z  \end{array}$
 This works: $\begin{matrix} \log_2(n!) &= &\log_2(n) + &\log_2(n-1) + &\log_2(n-2) + &... + &\log_2(1) \\ &< &\log_2(n) + &\log_2(n) + &\log_2(n) + &... + &\log_2(n) \\ &= &n \log_2(n) \end{matrix}$ $\begin{matrix} \log_2(n!) &= &\log_2(n) + &\log_2(n-1) + &\log_2(n-2) + &... + &\log_2(1) \\ &< &\log_2(n) + &\log_2(n) + &\log_2(n) + &... + &\log_2(n) \\ &= &n \log_2(n) \end{matrix}$ This doesn't work: \begin{align} \log_2(n!) &= \log_2(n) + \log_2(n-1) + \log_2(n-2) + ... + \log_2(1) \\ &< \log_2(n) + \log_2(n) + \log_2(n) + ... + \log_2(n) \\ &= n log_2(n) \end{align}  \log_2(n!) &= \log_2(n) + \log_2(n-1) + \log_2(n-2) + ... + \log_2(1) \\ &< \log_2(n) + \log_2(n) + \log_2(n) + ... + \log_2(n) \\ &= n log_2(n) \end{align}