Log

$a^{2}b=ab^{3} => a=b^{2} =>log b^{5}=1, log (ab)=log (b^{3})=3 \times 1/5$

$log(a^2 b)$ = 1
$a^2 b$ = 10
b = $\frac{10}{a^2}$ ......(1)
$log(ab^3)$ = 1
$ab^3$ = 10
a = $\frac{10}{b^3}$ ............(2)
Substituting value of 'a' in equation (1) , we get,
$b^5$ = 10 ........(3)
Substituting value of 'b' in equation (2) , we get, $a^5$ = 100 ...........(4)
Multiplying Equation (3) and (4) , we get,
( $a^5$ ) x ( $b^5$ ) = 1000
Putting Log on both the sides, we get,
$log (ab)^5$ = 3
$5 log (ab)$ = 3
$log(ab)$ = $\frac{3}{5}$