Question

State whether true or false:

Given that $x,y$ and $z$ are integers and ${10}^x=\left(4^y\right)\left(5^z\right)$ then, $x$ is even.

• A. True
• B. False

Answer 1

The correct option is A True

$(2\times 5{)}^x=(2^2{)}^x\times 5^z=2^{2y}\times 5^z$.

This tells you that x = 2y and x = z. (You need the same number of 2's and the same number of 5's on either side of the equation.) Since you know y is an integer, x must be even, because x = 2y.