Question

# The number of integral value(s) of $$x$$ satisfying the equation $$\left | x^{4}\cdot3^{\left | x-2 \right |}\cdot5^{x-1} \right |=-x^{4}\cdot3^{\left | x-2 \right |}\cdot5^{x-1}$$, is

A
2
B
3
C
1
D
infinite

Solution

## The correct option is C $$1$$The two sides of the equation are always of opposite signs.The left hand side is under modulus and is therefore always positive.$$x^4$$, $$3^{|x-2|}$$ and $$5^{|x-1|}$$ are always positive. Therefore, the right hand side is always negative.Hence, the only possible solution is when $$x=0$$Maths

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