Question

When log base b of 2=m and lob base b 3=n find the value of log base b of square root of 18

Answer 1

Hi,

Explanation:

`Two\ things\ to\ remember:\\log(u*v)=log(u)+log(v)\\log(u^v)=v*log(u)\\\\and\\√(x) =x^{(1)/(2)} \\\\log_b(2)=m\\log_2(3)=n\\\\√(18) =√(9*2) =3*√(2) \\\\log_b√(18) =log_b(3*√(2) )=log_b(3)+(1)/(2) log_b(2)=\boxed{n+(m)/(2) }`