Hi Gregory -
To solve this problem you need to "free up" the variable x from the log function and the best way to do this is to exponentiate both sides using the base of 10. (I'm assuming your notation log10 equals "log base 10")
10^[log10(4+x)] = 10^(1.1)
This results in 4+ x = 10^(1.1)
Now just solve for x and make sure the answer is valid by plugging back into the original equation.
Hope this helps