Question

Demonstrati ca numarul a=lg30+lg2-lg6este natural.

Answer 1

$a = \lg30+\lg2 -\lg 6 = \lg\Big(\dfrac{30\cdot 2}{6}\Big) = \lg\Big(\dfrac{60}{6}\Big) = \lg 10 = 1 \in \mathbb{N}$

$\lg a+\lg b = \lg(a\cdot b)\\ \\ \lg a - \lg b = \lg\Big(\dfrac{a}{b}\Big)$