Example 4 Calculate $7^{1 \lg 20} \cdot\left(\frac{1}{2}\right)^{\lg 0.7}$.

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Example 4 Calculate $7^{1 \lg 20} \cdot\left(\frac{1}{2}\right)^{\lg 0.7}$.
Solution 1: Let $7^{\lg 20} \cdot\left(\frac{1}{2}\right)^{\lg 0.7}=x$, then
so
$$
\begin{aligned}
\lg x & =\lg \left[7^{\lg 20} \cdot\left(\frac{1}{2}\right)^{\lg 0.7}\right] \\
& =(\lg 20 \cdot \lg 7)+\left(\lg 0.7 \cdot \lg \frac{1}{2}\right) \\
& =(\lg 2+1) \cdot \lg 7-(\lg 7-1) \cdot \lg 2 \\
& =\lg 14, \\
x & =14 .
\end{aligned}
$$

Solution 2: Use the conclusion $a^{\lg b}=b^{\lg a}$ to simplify.