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The number of value(s) of x satisfying t...

The number of value(s) of x satisfying the equation `(2011)^x+ (2012)^x + (2013)^x -(2014)^x=0` is/are :

Text Solution

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`(2011)^x+(2012)^x+(2013)^x - (2014)^x = 0`
`=> (2011)^x+(2012)^x+(2013)^x = (2014)^x`
If we draw the graph of `2011^x,2012^x and 2013^x`, we will find that their sum will match exactly one time with the `2014^x`.
Please refer to video to see the graph.
Thus, there will be exactly one solution fo the given equation.
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