How many roots does the following equation have:

$$
10^{\lg \cos x}=\frac{1}{7} x-1 ?
$$
The left side of the equation was incorrectly transformed by many. The equality $10^{\lg \cos x}=\cos x$ is only true if $\cos x>0$. After this, for example, we can graphically determine the number of roots, which is 3.