Question

Given: $x,y$ and $z$ are integers and $3^{x+5}={27}^{y+1}$, then $x$ is even.

• A. True
• B. False

Answer 1

The correct option is B False

$3^{x+5}={27}^{y+1}.$ You can again break the bases down into prime factors: $3^{x+5}=(3^3{)}^{y+1}$, so $3^{x+5}=3^{3(y+1)}$. This tells you that $x+5=3y+3$, so $x=3y-2$. (Again,you need the same number of 3's on either side of the equation.) Since y is an integer, x must be 2 smaller than a multiple of 3, but that does not tell you whether x is even. If $y=1$, then $x=1$ (odd), but if $y=2$, then $x=4$ (even).