To solve this equation, we need to first simplify the expression on the left side of the equation:
(10 ^ (5-x) )^ (6-x) = 100(10 ^ (5-x) * (6-x)) = 10010 ^ (30 - 11x + x^2) = 10010 ^ (x^2 - 11x + 30) = 100x^2 - 11x + 30 = log10(100)x^2 - 11x + 30 = 2x^2 - 11x + 28 = 0(x-4)(x-7) = 0x = 4 or x = 7
Therefore, the solutions to the equation are x = 4 or x = 7.
To solve this equation, we need to first simplify the expression on the left side of the equation:
(10 ^ (5-x) )^ (6-x) = 100
(10 ^ (5-x) * (6-x)) = 100
10 ^ (30 - 11x + x^2) = 100
10 ^ (x^2 - 11x + 30) = 100
x^2 - 11x + 30 = log10(100)
x^2 - 11x + 30 = 2
x^2 - 11x + 28 = 0
(x-4)(x-7) = 0
x = 4 or x = 7
Therefore, the solutions to the equation are x = 4 or x = 7.