Solve equation

2log10^x - 3log10^2 + 3log10^32 = 2

use your log rules

2log10^x - 3log10^2 + 3log10^32 = 2
2xlog 10 - 6log10 + 96log 10 = 2
we know log10 = 1, so...
2x - 6 + 96 = 2
2x = -88
x = -44