G4.3 Let $2^{x}=7^{y}=196$. If $T=\frac{1}{x}+\frac{1}{y}$, find the value of $T$.
$$
\begin{array}{l}
x \log 2=y \log 7=\log 196 \\
x=\frac{\log 196}{\log 2}, y=\frac{\log 196}{\log 7} \\
T=\frac{1}{x}+\frac{1}{y}=\frac{\log 2+\log 7}{\log 196}=\frac{\log 14}{\log 14^{2}}=\frac{1}{2}
\end{array}
$$

Method 2 (provided by Denny)
$$
\begin{array}{l}
2=196^{\frac{1}{x}}, 7=196^{\frac{1}{y}} \\
2 \times 7=14=196^{\frac{1}{x}} \times 196^{\frac{1}{y}}=196^{\frac{1}{x}+\frac{1}{y}} \\
\frac{1}{x}+\frac{1}{y}=\frac{1}{2}
\end{array}
$$