Let $B$ be the Meissel-Mertens constant, and $\theta(x)$ be Chebyshev's first function. Would there exist an $x_0$ such that for all $x>x_0$ the following inequalities are true (clearly, if the first one is true, so is the second one)? Can $x_0=3$? if not, 121?

1) $\int_2^x \frac{\theta(y)(1+\log y)}{y^2\log^2 y}dy-\log\log x>B$

2) $\int_2^x \frac{\theta(y)(1+\log y)}{y^2\log^2 y}dy-\log\log x+\frac{1}{\log x}>B$