what am I doing wrong in this algebra problem. (Logs)?

Question

1.) 10 ^ 2+x = 200

I started with (2+x) log10 = log 200
then went 2+x = log200
my answer was x=log200 / log 12

WHat should I do with the log10, the book showed to just get rid of it?

Answer 1

log 10 = 1, so yes, the book is correct. Just get rid of it.

10 ^ 2+x = 200
log (10^(2+x)) = log 200
2 + x = log 200
2 + x = log (2 * 100) = log 2 + log 100 (Rule: log ab = log a + log b)
2 + x = log 2 + 2
x = log 2 (solution!)