Linear Regression

This might make the difference between a B+ and an A for me. Please take a look.

Is the following a general linear regression model?
Y=\log_{10} (\beta_1 X_{i1}) + \beta_2 X_{i2} + \epsilon_i

I (and the instructor solutions manual) say "Yes"; however, it was marked wrong. Is it?

There's a log in there acting on one of the variables, so I'm guessing it's not anything having to do with "linear", but I really don't know.

Does the solutions manual have an explanation of the answer?