CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

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


A
0
loader
B
1
loader
C
2
loader
D
3
loader

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

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image