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

Solution

## 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, $$a\neq0$$, 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,$$a^b=4-ab$$$$a^1=4-a\times1$$$$a=4-a$$$$a=2$$Hence, option C is correct.Mathematics

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