Question

Given that log 2 = and log 3 = , express the following in terms of and

a) log72
b) log√27
c) log360

Answer 1

a) 3a+2b

b) 3/2b

c) 2a+2b+1

Explanation:

let, log2=a. log3=b

`log72=log(2^(3)*3^(2)) =log2^(3)+log3^(2)=3log2+2log3=3a+2b\\log√(27) =log\sqrt{3^(3)}=log3^(3/2)=(3)/(2)log3= (3)/(2)b\\log360=log{6^(2)*10}=log2^(2)*3^(2)+log10=2log2+2log3+1=2a+2b+1`