Question

If $\log 2=0.3010$ and $\log 3=0.4771$, then the value of $\log 3.6$ is $0.55a2$. where a is 3rd digit of the given value,then $a=?$

Answer 1

$x=\log 3.6$
$\therefore x=\log 36-\log 10$
$\therefore x=2\log (2\cdot 3)-1$ ...$\log a^b=b\log a$
$\therefore x=2\log 2+2\log 3-1$ ..$\log (a\cdot b)=\log a+\log b$
$\therefore x=2\log 2+2\log 3-1$ ...($\log a^b=b\log a$)
$\therefore x=2\times (0.3010+0.4771)=0.5562$