Solve 5 log 2x - log x - log 4x^2 *log to the base of 10 btw* Could anyone out there explain to me how to solve this in detail, please?

You can finish taking the logarithms and see what falls out. You know that
  log(ax^b) = log(a) + b*log(x)
Using this, you can simplify your expression as follows
  5log(2x) - log(x) - log(4x^2)
  = 5(log(2) + log(x)) - log(x) - (log(4) + 2log(x))
  = 5log(2) - log(4) + 5log(x) - log(x) - 2log(x)
We know 4 = 2^2, so log(4) = 2log(2).
  = 3log(2) + 2log(x)
  = log(2^3*x^2)
  = log(8x^2)
All you can do is simplify the expression. There is not enough information to determine a value for x.