Solving $2^x \cdot 5^y = 0,128$ $x,y \in \mathbb Z$
$2^x \cdot 5^y = 0,128$
$x+y = ?$
My attempt: 
I know that
$$0,128 = \frac{128}{1000}$$
$$5^3 = 125$$
$$2^{-3} = \frac{1}{8}$$

EDIT: 
$2^7 = 128$
Then we need to get 
$0,128$

You can write 5 in terms of 10 and 2... so you can write the problem as:
$2^x \cdot (\frac{10}{2})^y=.128$
$2^{x-y} \cdot 10^y=.128$
Find $y$ first and then $x $
