How do I solve log base 10 square root 2

Question

I have a calculus assignment and this is one of the questions, but I am not allowed a calculator.

Answer 1

log √2 = log 2^0.5 = 0.5 log 2  (using log to mean base 10, 'common log'; also relies on square root ⇔ exponent ½)

 

That's all you can do, unless you know, as I do, that log 2 = 0.30103 (because when I took Algebra Ii in 1952, we used a table of logarithms, and this fact lodged  in my brain also, log 3 = 0.47712.)

 

So answer should be ½log2.