1. Solve the inequality $\lg \left(5^{x}+x-20\right)>x-x \lg 2$.
Solution. Since

$$
x-x \lg 2=x(\lg 10-\lg 2)=x \lg 5=\lg 5^{x}
$$

The inequality takes the form

$$
\lg \left(5^{x}+x-20\right)>\lg 5^{x}
$$

From this

$$
5^{x}+x-20>0,5^{x}+x-20>5^{x}, \text{ so } x>20
$$