Functions question bank (Mathematics)

If $D_{30}$ is the set of all divisors of $30, x, y \in D_{30}$, we define $x+y=\operatorname{LCM}(x, y), x \cdot y=\operatorname{GCD}(x, y)$, $x^{\prime}=\frac{30}{x}$ and $f(x, y, z)=(x+y) \cdot\left(y^{\prime}+z\right)$, then $f(2,5,15)$ is equal to

The value of $\Delta \log f(x)+\Delta^{2}\left(3^{x}\right)$ is