log 2x + log x = 5

Using the Product Property log (2x*x) = log (2x^2) = 5

Using definition of log 2x^2 = 10^5 ---> 2x^2 = 100,000

Divide both sides by 2

x^2 = 50,000 Take the square root of both sides.

x = + or - 223.6 (That's approximate. It's exactly + or - sqrt(50000))

You can ignore the negative solution unless you're dealing with imaginary numbers.
To check, plug 223.6 back into the equation. You'll see it works.