Question

Prove the above question

Answer 1

Final Answer : x =4 , 0
Q :
${ |1 - x| }^{ log_{10}( {x}^{2} - 5x + 5) } = 1$
Find Solution ?

Steps :
1) Either
$|1 - x| = 1 \\ = > x = 0$
or
$log_{10}( {x}^{2} - 5x + 5 ) = 0 \\ = > {x}^{2} - 5x + 5 = {10}^{0} \\ = > {x}^{2} - 5x + 5 = 1 \\ = > {x}^{2} - 5x + 4 = 0 \\ = > (x - 4)(x - 1) = 0 \\ = > x = 4 \: \: or \: x \: = 1$
We rejected x = 1 as base becomes 0.
And |1-x| becomes non differentiable function at x = 1 .
So, Finally
Solution set x = 0,4