If 1- _ 10 2= _ 10 (5^x+4^x+3^x+2^x+1) , then what is a value of x ?

The given equation is $1 - \log_{10}2 = \log_{10}(5^x + 4^x + 3^x + 2^x + 1)$

Simplifying the left hand side:

$1 - \log_{10}2 = \log_{10}10 - \log_{10}2 = \log_{10}\left(\dfrac{10}{2}\right) = \log_{10}5$

Equating this to the right hand side:

$\log_{10}5 = \log_{10}(5^x + 4^x + 3^x + 2^x + 1)$

Since the logarithmic function is one-to-one, we can equate the arguments:

$5 = 5^x + 4^x + 3^x + 2^x + 1$

$5^x + 4^x + 3^x + 2^x = 4$

Substituting $x = 0$ into the equation:

$5^0 + 4^0 + 3^0 + 2^0 = 1 + 1 + 1 + 1 = 4$

Thus, $x = 0$ satisfies the equation.

Answer: $0$