The number of values of x satisfying
`2^(log_5 16. log_4 x +x log_2 5) + 5^x + x^((log_5 4)+5) + x^5 = 0`

Answer

0

Explanation

`2^(2log_(5)4.log_(4)x+xlog_(2)5)+5^(x)+x^(5).x^(log_(5)4)+x^(5)=0`
`2^(2log_(5)x)xx2^(xlog_(2)5)+5^(x)+x^(5)(4^(log_(5)x)+1)=0`
`5^(x)(2^(log_(5)x))^(2)+5^(x)+x^(5)((2^(log_(5)x))^(2)+1)=0`
`(5^(x)+x^(5))(((2^(log_(5)x))^(2)+1),("Always "gt-))=0`
`5^(x)+x^(5)=0" Only for "xlt0`
Only solution can be for `xlt0`
But for log to define `x gt0`
So, no solution exists