Problem (Algebra):
Let $T=T N Y W R$. Compute $2^{\log _{T} 8}-8^{\log _{T} 2}$.

Solution:
Let $\log _{T} 8=x$. Then $T^{x}=8$. Thus the given expression equals $2^{x}-\left(T^{x}\right)^{\log _{T} 2}=2^{x}-T^{x \log _{T} 2}=$ $2^{x}-T^{\log _{T} 2^{x}}=2^{x}-2^{x}=\mathbf{0}$ (independent of $T$ ).

Final answer: 0