Question

If $a^b=4-ab$ and $b^a=1$, where $a$ and $b$ are positive integers, find $a$.

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is C $2$

Plug in real numbers for $a$ and $b$. Since it isn’t clear what numbers to plug in to satisfy the first equation, look at the second equation instead. First, realize that $a$ cannot be $0$ since a is a positive integer.
Since, $a\ne 0$, so the only way to get $b^a=1$ is if $b=1$(As $1$ to any power is $1$).
Plugging $b=1$ in to the first equation,
$a^b=4-ab$
$a^1=4-a\times 1$
$a=4-a$
$a=2$
Hence, option C is correct.