Steel

I'm still rather confused but I did get the correct result. Can you tell me if I've done it correctly or not?

13.8= 5 lg 1000r/10 + r

13.8 = 5 lg 100r + r

-5 lg 100r = r - 13.8

lg 100r = -0.2r + 2.76

2 lg r = -0.2r + 2.76

lg r = -0.2r + 2.76 - 2

lg r = -0.2r + 0.76

I have an equation 13.8 = 5 lg 1000r / 10 + r. I know this can be written as lg r = -0.2r + 0.76 but I cannot figure out how this is achieved. It's been forever since I've done any maths and honestly I seem to have forgotten a lot about what I learned at school

Could someone do a step by step demonstration of how to get from the first equation to the second so I would understand where the 'result' comes from. Thank you!