Beginners calculation with logarithms

Question

Given that $\log_{10}2 =0.3010$ and $\log_{10}3 = 0.4771$, evaluate the following without using mathematical tables or calculators

$(a) \log_{10} 81 $
$(b)\log_{10} 40 $

Answer 1

By using various rules of logarithms, we have $$\log_{10}(40)=\log_{10}(2^2\cdot 10)=\log_{10}(2^2)+\log_{10}(10)=2\log_{10}(2)+1.$$

I'm sure you can do the first one by a similar decomposition.